Answer:
x² - 20 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{( {b})^{2} - 4ac } }{2a} [/tex]
a = 1 b = 0 c = -20
So we have
[tex]x = \frac{ - 0 ± \sqrt{ {0}^{2} - 4(1)( -20)} }{2(1)} \\ \\ x = \frac{± \sqrt{80} }{2} \\ \\ x = \frac{±4 \sqrt{5} }{2} \\ \\ \\ x = ±2 \sqrt{5} \\ \\ \\ x = 2 \sqrt{5} \: \: \: or \: \: \: x = - 2 \sqrt{5} [/tex]
Hope this helps you.
Explain why f(x) = x^2-x-6/x^2-9 is not continuous at x = 3.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Required
Why is the function not continuous at x = 3
First substitute 3 for x at the denominator
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Factorize the numerator and the denominator
[tex]f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}[/tex]
[tex]f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}[/tex]
[tex]f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}[/tex]
Divide the numerator and denominator by (x - 3)
[tex]f(x) = \frac{x+2}{x+3}[/tex]
Substitute 3 for x
[tex]f(3) = \frac{3+2}{3+3}[/tex]
[tex]f(3) = \frac{5}{6}[/tex]
Because [tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex] is defined when x = 3;
Then the function is continuous
Answer:
A: f is not defined at x = -3
Step-by-step explanation: EDGE 2020
Can someone help me solve this :): ?
( brainliest to the correct answer/explanation)
Answer:
1and1/2yrs ago
Step-by-step explanation:
price dis year= 56545
reduction per year= 11309
...number of years ago = 73810-56545=17265
and is about 20% of annual deductions
so if 56545 +20% + 1/2 20% = 1nd1/2 yrs
Rewrite the equation y= 4/5.x + 3 in general form Ax + By + C = O
Work Shown:
y = (4/5)x + 3
5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction
0 = 4x + 15 - 5y ... subtract 5y from both sides
4x-5y+15 = 0 .... rearrange terms
The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.
Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.
graph the circle x2 + y2 - 12x + 6y +36 =0
x^2+y^2-12x+6y+36=0
Top Point: (6,0)
Left Point: (3,-3)
Right Point: (9,-3)
Bottom Point: (6,-6)
Answer:
[tex] x^2 +y^2 -12x +6y +36 =0[/tex]
And we can complete the squares like this:
[tex] (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2[/tex]
And we got:
[tex] (x-6)^2 + (y+3)^2 = 9[/tex]
And we have a circle with radius r =3 and the vertex would be;
[tex] V= (6,-3) [/tex]
The graph is on the figure attached.
Step-by-step explanation:
For this case we have the following expression:
[tex] x^2 +y^2 -12x +6y +36 =0[/tex]
And we can complete the squares like this:
[tex] (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2[/tex]
And we got:
[tex] (x-6)^2 + (y+3)^2 = 9[/tex]
And we have a circle with radius r =3 and the vertex would be;
[tex] V= (6,-3) [/tex]
The graph is on the figure attached.
Item 25 The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function. 0 1 2 3 4 5 6 7 8 9 10
Answer:
[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]
Step-by-step explanation:
Given
[tex]m = 45 - 7.5b[/tex]
[tex]Values: \{0,1,2,3,4,5,6,7,8,9,10\}[/tex]
Required
Select all values that belongs to the domain of the given function
Analyzing the question;
The question says that the function, m represent the amount left after buying b number of books
This means that, after purchasing b books, I'm expected to have a certain m amount of dollars left with me;
This implies that the value of m can never be negative;
So, the domain of m are values of b such that [tex]m \geq 0[/tex]
When b = 0
[tex]m = 45 - 7.5(0)[/tex]
[tex]m = 45 - 0[/tex]
[tex]m = 45[/tex]
When b = 1
[tex]m = 45 - 7.5(1)[/tex]
[tex]m = 45 - 7.5[/tex]
[tex]m = 37.5[/tex]
When b = 2
[tex]m = 45 - 7.5(2)[/tex]
[tex]m = 45 - 15[/tex]
[tex]m = 30[/tex]
When b = 3
[tex]m = 45 - 7.5(3)[/tex]
[tex]m = 45 - 22.5[/tex]
[tex]m = 22.5[/tex]
When b = 4
[tex]m = 45 - 7.5(4)[/tex]
[tex]m = 45 - 30[/tex]
[tex]m = 15[/tex]
When b = 5
[tex]m = 45 - 7.5(5)[/tex]
[tex]m = 45 - 37.5[/tex]
[tex]m = 7.5[/tex]
When b = 6
[tex]m = 45 - 7.5(6)[/tex]
[tex]m = 45 - 45[/tex]
[tex]m = 0[/tex]
When b = 7
[tex]m = 45 - 7.5(7)[/tex]
[tex]m = 45 - 52.5[/tex]
[tex]m = -7.5[/tex]
There's no need to check for other values, as they will result in negative values of m;
Hence, the domain of m are:
[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]
The values that are in the domain of the function are 7, 8, 9 and 10
Linear functionsGiven the linear function m=45−7.5b
where:
b represents the amount m (in dollars) of moneyFor th domain to exist, then;
45 - 7.5b< 0
7.5 b > 45
b > 45/7.5
b > 6
Hence the values that are in the domain of the function are 7, 8, 9 and 10
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Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation? because both triangles appear to be equilateral because∠MNL and ∠ONP are congruent angles because one pair of congruent corresponding angles is sufficient to determine similar triangles because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
Answer:
The correct option is;
Because ∠MNL and ∠ONP are congruent angles
Step-by-step explanation:
From the diagram shown in the question, ∠MNL and ∠ONP are vertically opposite angles as they are formed by crossing of the lines LP and MO making them congruent, that is ∠MNL ≅ ∠ONP
Given that two angle of triangle LMN are congruent to two angles of triangle PON , then by the Angle Angle (AA) rule of similarity, triangle LMN and PON are similar.
The information in the diagram enough to determine that △LMN ~ △PON because∠MNL and ∠ONP are congruent angles.
What are Congruent angles?These are referred to angles which have an equal measure. From the diagram ,vertically opposite angles are formed by crossing of the lines LP and MO thus,we can deduce that ∠MNL and ∠ONP are congruent angles.
This means that there is enough information to determine that △LMN ~ △PON using a rotation about point N and a dilation.
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Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased
Answer:
[tex]\large \boxed{87.5 \, \%}[/tex]
Step-by-step explanation:
Let x = the original number of books
Then 0.375x = the total number of biographies
and 0.20 x = the original number of biographies
[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]
For what value of x does 5^x-2 not equal zero?
a. all except 2
b. all except 0
c. all except -4
d. all except -2
e. all real numbers
Answer:
E: all real numbers
Step-by-step explanation:
Which expression is equivalent to 10 to the 4 power? A.) 10 times 10 times 10 times 10 B.) 40 C.) 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4 D.) 4,444,444,444
Answer:
A
Step-by-step explanation:
Here in this question, we want to select which of the options particularly represents what was given in the question.
Mathematically 10^4 means that we are raising 10 into a continued exponential raising up to 4 times.
So 10^4 is pronounced as the first option in the question.
10 raised to power 10 , raised to power 10 etc
Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if exactly two of the triplets are in the starting lineup?
Answer:
990 ways to choose 6 starters out of 14 with exactly two of the three triplets.
Step-by-step explanation:
Ways to choose 2 of the triplets
= C(3,2) = 3! / (2!1!) = 3
Ways to choose the remaining 4 starters out of 11 players left
= C(11,4) = 11! / (4!7!) = 330
Total number of ways to choose 6 starters
= 3*330 = 990
Which statements are true regarding undefinable terms in geometry?
C. A line has one dimension, length.
E. A plane consists of an infinite set of lines.
Write an equation of a line with the given slope and y-intercept. m = 1, b = 4 a) y = x – 4 b) y = –1x + 4 c) y = x + 4 d) y = 4x + 1
Answer:
y = x+4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 1x+4
y = x+4
Answer:
[tex]\boxed{y=x+4}[/tex]
Step-by-step explanation:
The slope-intercept form of a line:
[tex]y = mx+b[/tex]
m is the slope and b is the y-intercept
[tex]m=1\\b=4[/tex]
[tex]y = 1x+4[/tex]
The distance from Parrot Point Airport to the Ivy Cliffs is 178 miles at and angle of 7.1 degrees northeast. There is a wind blowing southeast at 30 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly? * Round the speed to the nearest tenth of a mile per hour and angle to the nearest tenth of a degree. Where north is 0 degrees and positive is clockwise.
Answer:
The speed is 74.0 miles per hour and the angle is 65.1° north-east
Step-by-step explanation:
We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.
Since the wind is moving south east, it is at 45 south of east or a bearing of 135.
Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles
Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles
The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles
The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles
The total vertical displacement of the plane is 176.64 miles - 42.43 miles = 134.21 miles
The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles
The direction of this displacement is thus
Ф = tan⁻¹(total vertical displacement/total horizontal displacement)
= tan⁻¹(134.21/62.43)
= tan⁻¹(2.1498)
= 65.05°
= 65.1° to the nearest tenth degree.
The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.
So the speed is 74.0 miles per hour and the angle is 65.1° north-east
The function f(t) = -6r+ 11 has the range {- 37. - 25. - 13, -1). Select the domain values from the list
1. 2. 3. 4. 5. 6. 7. 8. Justify your choices by explaining how you determined the domain values.
answer
-6r+-11=-37
-6r=-37+11
-6r=-48
r=8
A penny is dropped from a height of 144 feet. Calculate the time between when the rock was dropped and when it landed. If we choose
"down" as positive and ignore air friction, the function is h(t) 16t2 - 144.
Answer:
3 seconds
Step-by-step explanation:
Given the function :
h(t) = 16t2 - 144.
h = height = 144 and t = time after t seconds the ball penny was dropped.
When the penny lands, h = 0
Therefore, our function becomes ;
16t2 - 144 = 0
The we can solve for t
16t^2 - 144 = 0
16t^2 = 144
Divide both sides by 16
(16t^2 / 16) = 144 / 16
t^2 = 9
Take the square root of both sides
t = 3
Therefore, the time between when the rock was dropped and when it landed is 3seconds
Answer:
t = 3 seconds
Step-by-step explanation:
if an article is sold with 20% discount,there will be a profit of 15%.If it is sold at 10% discount, there will be a profit of Rs.200.Calculate the market price of an article
Answer:
The market price of the article is Rs. 978.72
Step-by-step explanation:
Let x represents the market price.
Let y represents the selling price.
Let z represents the cost price.
if an article is sold with 20% discount then there will be a profit of 15%.
SP = CP+Profit =z+0.15z=1.15z
ATQ
[tex]0.80x = 1.15z\\0.80x- 1.15z = 0[/tex]
If it is sold at 10% discount then there will be a profit of Rs.200
ATQ
[tex]0.9x - z = 200[/tex]
Now we are supposed to find the market price of an article.
[tex]0.9x - z= 200[/tex]
Multiplying 1.15 both sides
[tex]0.9x \times 1.15 - 1.15z = 200 \times 1.15\\1.035x - 1.15z = 230[/tex]
We know that[tex]1.15z = 0.80x[/tex]
[tex]1.035x - 0.80z = 230\\0.235x = 230\\x = \frac{230}{0.235}\\x= Rs. 978.72[/tex]
Hence The market price of the article is Rs. 978.72
An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid has base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Answer:
volume of trapezoidal prism = 15x^2 cubic units
Step-by-step explanation:
First, area of the trapezoidal bases.
Parallel sides measure x and 2x, for an average of 1.5x.
Height = x
Area of trapezoidal base = 1.5x*x = 1.5x^2
Volume of prism = area base * height
(length does not matter, height does)
= 1.5x^2 * 10 = 15x^2
The volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
An oblique prism has trapezoidal bases and a vertical height of 10 units.
As we know, the area of the trapezoidal bases:
From the figure:
Height = x
Area of trapezoidal base = (1.5x)(x) = 1.5x²
The volume of prism = area base×height
= 1.5x²×10 = 15x² cubic units
Thus, the volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
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Given the sequence -3, 9, -27, 81, -243, ..., find the recursive formula.
Answer:
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex]
Step-by-step explanation:
There is a common ratio between consecutive terms of the sequence, that is
r = 9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 243 ÷ 81 = - 3
The recursive formula is of the form
[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex] = - 3[tex]a_{n-1}[/tex]
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,600. A random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05. The confidence interval for this hypothesis test would be ________.
Answer:
A 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].
Step-by-step explanation:
We are given that a random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average debt load = $18,800
[tex]\sigma[/tex] = population standard deviation = $4,800
n = sample of students = 28
[tex]\mu[/tex] = population average debt load
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 5% level of
significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]\$18,800-1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] , [tex]\$18,800+1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] ]
= [$17,022.05, $20,577.94]
Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].
plz help, will give brainiest
(08.01, 08.02, 08.03 HC)
Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)
Answer:
4x^2 + 8x + 4
4(x^2 + 2x + 1) - remove GCF of 4
4(x + 1)(x + 1) - factor
4(x + 1)^2 - collect like terms
Step-by-step explanation:
Then also expand it out by distributing:
21x^3 + 35x²
Form 1:
21x^3 + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
Update:
You could also multiply two binomials and make a quadratic.
Example:
(7x + 2)(3x + 5)
7x(3x + 5) + 2(3x + 5)
= 21x² + 35x + 6x + 10
= 21x² + 41x + 10
The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.
What is a polynomial?
A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The polynomial will be solved as below:-
21x³ + 35x²
Form 1:
21x³ + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
You could also multiply two binomials and make a quadratic.
E = (7x + 2)(3x + 5)
E = 7x(3x + 5) + 2(3x + 5)
E = 21x² + 35x + 6x + 10
E = 21x² + 41x + 10
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Is the following relation a function?
Answer:
No, Given relation is not a function.Explanation:
We know that , if any vertical line cuts the given graph of relation at exactly one point, then the relation can be called as function.
From Given graph , we find that the vertical line through any point on x-axis greater than zero (ex : X = 5) cuts the graph at more than one point.
Hence, Given relation is not a function.
Hope this helps...
Good luck on your assignment...
WILL MARK BRAINLIEST!!!!!!!! :))))))))))))))))
Answer:
(A) No solution
(B) One solution
(C) One solution
(D) One solution
(E) No solution
Please tell me if this is incorrect. I hope this helps!
I need help i will mark brainliest please
Answer:
1) true
2) false
hope it worked
and pls mark me as BRAINLIEST
The population of a city increase exponentially at a rate of x% every 5 years
In 1960 the population was 60100
In 2015 the population was 120150
Calculate the value of x
Answer:
1.1460277. Put in your decimal place given to you.
This is the percentage rate.
Step-by-step explanation:
f(x)=0=60100
55=120150
60100=a*b^0
120150/60100=60100/60100*b^5
b^5^(1/5)=5square root(120150/60100)=1.14860277
Romeo is using a common algorithm to find the product of 8,125 × 9. Drag the correct numbers to the problem to show the partial products and to complete the multiplication for Romeo.
Answer:
its harddd
Step-by-step explanation:
rightttttttt
What is the slope of the graph?
Answer:
-2
Step-by-step explanation:
The slope formula is
m = ( y-2-y1)/(x2-x1)
Using two points on the line (0,4) and (2,0)
m = ( 0-4)/(2-0)
= -4/2
=-2
Answer:
-2
Step-by-step explanation:
Slope is change in y over change in x
the change in y is -2 and the change in x is 1 so you do -2/1 and that as a whole number is -2.
Please help me with this problem! If anybody answers first in this, i will give brainliest to you! Be the first one to answer this then i will give out a brainliest award to you!
Are you sure your that person?
Answer:
32 remainder 2
Step-by-step explanation:
To divide 162 by 5, we simply do the following:
5 goes into 16 => 3
Multiply 5 by 3 => 3 × 5 = 15
Subtract 15 from 16 => 16 – 15 = 1
Put the 1 before 2 => 12
5 goes into 12 => 2
Multiply 5 by 2 => 5 × 2 = 10
Subtract 10 from 12 => 12 – 10 => 2
In summary,
162 divided by 5 => 32 remainder 2
Please see attached photo for further details.
Pls help me with this question
Answer:
[tex]\sqrt[5]{x^7}[/tex]
or (x ^ 1/5) ^7
or ([tex]\sqrt[5]{x}[/tex])^7
Step-by-step explanation:
x ^ 1.4
Rewriting the decimal as an improper fraction
x ^ 14/10
x ^ 7/5
The top is the power and the bottom is the root
[tex]\sqrt[5]{x^7}[/tex]
or (x ^ 1/5) ^7
or ([tex]\sqrt[5]{x}[/tex])^7
Adding Rational Numbers Using Properties of Operations we can
add integers in any order using the
and
properties of addition.
Consider the integers a, b, c, and -d. We can add this group of
integers in several different ways:
a + (-b) + C+ (-0)
a+c+ (-6) + (-d)
(a + c) + [(-b) + (-d)]
The sum of the integers remains the
regardless of
their arrangement. We can use the commutative and associative
properties to break up numbers by
to find the sum of two or more rational numbers.
Answer:
First blank: Commutative
Second blank: Associative
Third blank: Same
Fourth blank and fifth blank: Rearranging them? (Not entirely sure)
Hope this helps :)
factor x^5y^2+x^2y^5
Answer:
x^2y^2(x+y)(x^2-xy+y^2)
Step-by-step explanation:
x^5y^2+x^2y^5
Factor out the greatest common factor
x^2y^2( x^3+y^3)
Apply the Sum of Cubes Formula x^3+y^3 =(x+y)(x^2-xy+y^2)
x^2y^2(x+y)(x^2-xy+y^2)
Answer:
The answer is
x²y²( x + y)(x² - xy + y²)Step-by-step explanation:
[tex] {x}^{5} {y}^{2} + {x}^{2} {y}^{5} [/tex]
To factorize the expression first factor
x²y² out
We have
x²y²( x³ + y³)
Using the expression
a³ + b³ = ( a + b)(a² - ab + b²)Factorize the terms in the bracket
So we have
x³ + y³ = ( x + y)(x² - xy + y²)
Combine the expressions
We have the final answer as
x²y²( x + y)(x² - xy + y²)Hope this helps you