Factor the polynomial. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. x^3+216 this factors into:(Answer + Answer)(Answer - Answer+Answer)
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Answer:
[tex](x+6)(x^2-6x+36)[/tex]Explanation:
Given the expression
[tex]x^3+216\text{ }[/tex]This can also be written as:
[tex]x^3+6^3[/tex]Using the sum of cube identity
[tex]a^3+b^3=\mleft(a+b\mright)\cdot\mleft(a^2-ab+b^2\mright)[/tex]Comparing both expressions, we can see that:
a = x
b = 6
Substituting these parameters into the identity expression
[tex]\begin{gathered} x^3+6^3=(x+6)\cdot\mleft(x^2-6x+6^2\mright) \\ x^3+216=(x+6)(x^2-6x+36) \end{gathered}[/tex]This gives the required factor of the given expression
Related Questions
Which of the following logarithmic equations is equivalent to the exponentialequation below?8* -512A. log, 512 -B. 1096128 - XC. log, * - 512O D.log, 512 - 8
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Answer:
To find the eqivalent exponential equation to the following equation
[tex]8^x=512[/tex]we have that,
A mathematical notation of expressing a quantity as a number raised to the power of another number is called the exponential form and it is also called as exponential notation. According to the exponentiation, a quantity is split as factors on the basis of a number.
From the definition of exponential function, we have
[tex]a^x=y\text{ if and only if }\log _ay=x[/tex]For the given equation we get,
[tex]\log _{10}512=x[/tex]Answer is: option A:
[tex]\log _{10}512=x[/tex]What congruence rule does the triangle follow? Please write the congruence statement triangle HFD is congruent to ________? the congruence statement:Triangle HFD is congruent to Triangle ______
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In the given triangle HFD and triangle EDG
[tex]\begin{gathered} \angle HDF=\angle EDG\text{ ( Vertically Opposite Angle)} \\ \angle DFH=\angle DGE\text{ ( each of 90 degre}es) \\ HD=ED\text{ (Given)} \end{gathered}[/tex]Thus by Angle Angle Side Congurency (AAS) Triangle HFD and EDG are congurent
Answer:
the congruence statement triangle HFD is congruent to EDG
I need help with this, please help if you can.
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Let's put more details in the given figure:
Step 1: Let's first find x.
The total measure of a circle is 360°.
We get,
[tex]\text{ Arc LM + Arc MJ + Arc JR + x = 360}\degree[/tex][tex]\text{ 100}\degree\text{ + 72}\degree\text{ + 140}\degree\text{ + x = 360}\degree[/tex][tex]\text{ 312}\degree\text{ + x = 360}\degree[/tex][tex]\text{ x = 360}\degree\text{ - 312}\degree[/tex][tex]\text{ x = 48}\degree[/tex]
Step 2: Let's now find ∠K.
[tex]\text{ m\angle K = }\frac{1}{2}(Arc\text{ ML - x\rparen}[/tex][tex]\text{ = }\frac{1}{2}(72\text{ + 48\rparen = }\frac{1}{2}(120\degree)[/tex][tex]\text{ m\angle K = 60}\degree[/tex]Therefore, the measure of ∠K is 60°
When 4 digits between 0 and 9 are randomly selected with replacement for a lottery ticket, what is the probability that at least one digit is 7.
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We will have the following:
We will be able to take 4 values, so:
*When we pick value 1: There will be 10 possible choices [1/ 10]
*When we pick value 2: There will be 9 possible choices [1/9]
*When we pick value 3: There will be 8 possible choices [1/8]
*When we pick value 4: There will be 7 possible choices [1/7]
So, the probability of that number being seven is the following:
[tex]p=(\frac{1}{10})(\frac{1}{9})(\frac{1}{8})(\frac{1}{7})\Rightarrow p=\frac{1}{5040}\Rightarrow p=1.984126984\cdot10^{-4}[/tex]So, the probability of at least one digit is 7 is 0.0001984126984.
a grocery store is offering a promotion where a customer receives $0.20 discount per selected sale items, and Paulo has a coupon where he receives $0.10 off regularly priced items. Before applying the discounts the cost of Paulo's sale items was $58..18 and the cost of Paulo's regularly priced items was $ 41.34. After applying the discounts, Paulo spent $92.32 on both the sale items and regularly priced items. if Paulo bought 6 more sale items than regularly priced items, how many items did he buy in all?
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SOLUTION
Define a parameter
[tex]\begin{gathered} Sales\text{ item=X} \\ \operatorname{Re}gular\text{ items =y} \end{gathered}[/tex]Since Paulo have 6 more items, we have
[tex]\begin{gathered} y+6 \\ \text{and } \\ x-6 \end{gathered}[/tex]Then the equation becomes
[tex]undefined[/tex]
For the measured quantity, choose the set of numbers that is most appropriate to describe it. There is one correct answer.
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we have that
Area of circle --------> is a positive number
so
most appropriate is a natural number
answer is option C
On a recent day, 8 euros were worth $9 and 40 euros were worth $45. Enter an equation of the formy = kx to show the relationship between the number of euros and the value in dollars. Let y be the valuein dollars and x be the number of euros.The equation is y =
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The equation between number of euro and number of dollars will be in the form y = kx.
y is the value in dollars and x is the value in euros.
From the information given,
8 euro = 9 dollar
dividing by '8' we can say:
8/8 euro = 9/8 dollars
1 euro = 9/8 dollar
This is the value for k.
Thus, we have:
[tex]y=\frac{9}{8}x[/tex]We were given 8 euro = 9 dollar and 40 euro = 45 dollars. Let's see if they are correct using our equation:
[tex]\begin{gathered} y=\frac{9}{8}\times8 \\ y=9 \\ \text{Correct!} \\ y=\frac{9}{8}\times40 \\ y=45 \\ \text{Correct!} \end{gathered}[/tex]Thus the correct relationship is:
[tex]y=\frac{9}{8}x[/tex]Calculate the future value. (Round your answer to two decimal places.)P = $27,000, r = 7% compounded monthly, t = 6 years
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Answer:
Explanation:
Given:
Principal, P = $27,000
Rate, r = 7% = 0.07
Time, t = 6 years
Number of time compounded per year, n = 12.
We obtain the future value using the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values, we have:
[tex]\begin{gathered} A=27000(1+\frac{0.07}{12})^{12\times6} \\ \\ =A=27000(1+\frac{0.07}{12})^{72} \\ \\ =41042.85 \end{gathered}[/tex]Order from least to greatest 5.01, 5.01(with the little bar on top of the 1), 5.01(with the little bar on top of the 0 and 1), square root of 26
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Samuel, these are the numbers:
• 5.01
,• 5.01111111
,• 5.01010101
,• √26 = 5.09901
The least is 5.01 and the greatest is 5.09901, and 5.01111111 > 5.01010101
A rectangular garden plot has an area of 250 square ft. which of the following are possible dimensions for the plot? - 20 ft X 20 ft- 25 ft X 10 ft - 125 ft by 2ft - 5 ft X 50 ft
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Given:
A rectangular garden plot has an area of 250 square ft.
Required:
To choose the possible dimensions for the plot.
Explanation:
We know that the area of rectangle is,
[tex]A=l\times w[/tex]Now, consider the option (1)
[tex]\begin{gathered} 20ft\times20ft \\ =400\text{ sqr}ft \end{gathered}[/tex]Option(2):
[tex]\begin{gathered} 25ft\times10ft \\ =250sqrft \end{gathered}[/tex]Option(3):
[tex]\begin{gathered} 125ft\times2ft \\ =250sqrft \end{gathered}[/tex]Option(4):
[tex]\begin{gathered} 5ft\times50ft \\ =250sqrft \end{gathered}[/tex]Final Answer:
The possible dimension for the plot are,
- 25 ft X 10 ft
- 125 ft by 2ft
- 5 ft X 50 ft
s
solve problems 1/2÷ 2=
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Solve:
[tex]\frac{1}{2}\div2[/tex]Suppose we have 1 half of an orange:
So, slide the orange into two pieces::
Then, 1/2÷2=1/4.
Solve for x1/2x - 2 = 5
Answers
Answer:
x = 14
Explanation:
The given expression is
[tex]\frac{1}{2}x-2=5[/tex]To solve for x, we first need to add 2 to both sides
[tex]\begin{gathered} \frac{1}{2}x-2+2=5+2 \\ \\ \frac{1}{2}x=7 \end{gathered}[/tex]Then, we can multiply both sides by 2
[tex]\begin{gathered} 2\cdot\frac{1}{2}x=2\cdot7 \\ \\ x=14 \end{gathered}[/tex]Therefore, the answer is
x = 14
Fill in the blanks with the word bank at the bottom
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1. The average squared distance from each value from the mean is Variance
2. The middle value is Median
3. The average is Mean
4. Values that describe the centre data Measures of central tendency
5. The most repeated value is Mode
6. A value that describes how spread out a data is, is Measure of variation
7. The average distance of each value to the mean is Mean Absolute Deviation (MAD)
8. Square root of the variance is the Standard deviation
answer answer your answer by filling in the blank boxes
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We are given the following 2x2 matrix
[tex]A=\begin{bmatrix}{-3} & {-2} \\ {4} & {8}\end{bmatrix}[/tex]We are asked to find the inverse of matrix A.
Recall that the inverse of a 2x2 matrix is given by
[tex]A^{-1}=\frac{1}{ad-bc}\times\begin{bmatrix}{d} & {-b} \\ {-c} & {a}\end{bmatrix}[/tex]Where
a = -3
b = -2
c = 4
d = 8
Let us substitute these values into the above equation
[tex]A^{-1}=\frac{1}{(-3)(8)-(-2)(4)}\times\begin{bmatrix}{8} & {-(-2)} \\ {-(4)} & {-3}\end{bmatrix}[/tex]Now simplify
[tex]\begin{gathered} A^{-1}=\frac{1}{-24+8}\times\begin{bmatrix}{8} & {2} \\ {-4} & {-3}\end{bmatrix} \\ A^{-1}=\frac{1}{-16}\times\begin{bmatrix}{8} & {2} \\ {-4} & {-3}\end{bmatrix} \\ A^{-1}=\begin{bmatrix}{\frac{8}{-16}} & {\frac{2}{-16}} \\ {\frac{-4}{-16}} & {\frac{-3}{-16}}\end{bmatrix} \\ A^{-1}=\begin{bmatrix}{-\frac{1}{2}} & {-\frac{1}{8}} \\ {\frac{1}{4}} & {\frac{3}{16}}\end{bmatrix} \end{gathered}[/tex]Therefore, the inverse of the matrix A is
[tex]A^{-1}=\begin{bmatrix}{-\frac{1}{2}} & {-\frac{1}{8}} \\ {\frac{1}{4}} & {\frac{3}{16}}\end{bmatrix}[/tex]what the area of square 6/7 yd and 6/7
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The area of a square is it's length times it's width. Since in a square the length and the width are the same, the area is just the size of it's sides squared:
[tex]A=\text{side}^{2}[/tex]This square have sides of 6/7 yd, so the area is:
[tex]A=(\frac{6}{7}yd)^{2}=\frac{6^2}{7^{2}}yd^{2}[/tex][tex]A=\frac{36}{49}yd^{2}[/tex]Which number is between -8 and 5/4? -4.0, 1.3%, -0.1, -1/4, 3/2, 130% Help me!!
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5/4 = 1.25
1.3% = 1.3/100 = 0.013
-1/4 = -0.25
3/2 = 1.5
130% = 130/100 = 1.3
is -4 greater than -8? yes
is - 4 less than 1.25? yes
then, -4 is between -8 and 5/4
is 0.013 greater than -8? yes
is 0.013 less than 1.25? yes
then, 1.3% is between -8 and 5/4
is -0.1 greater than -8? yes
is -0.1 less than 1.25? yes
then, -0.1 is between -8 and 5/4
is -1/4 greater than -8? yes
is - 1/4 less than 1.25? yes
then, -1/4 is between -8 and 5/4
is 1.5 greater than -8? yes
is 1.5 less than 1.25? no
then, 3/2 isn't between -8 and 5/4
is 1.3 greater than -8? yes
is 1.3 less than 1.25? no
then, 130% isn't between -8 and 5/4
The graph of y = f(x) is shown in the xy-plane below.
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Let's put more details in the given graph,
We will generate the equation of the graph based on the following form:
[tex]\text{ f(x) = a(x - h)}^2\text{ + k}[/tex]We get,
[tex]\text{ f(x) = a(x - h)}^2\text{ + k}[/tex][tex]\text{ f(x) = a(x - 1)}^2\text{ + }(-9)[/tex][tex]\text{ f(x) = a(x - 1)}^2\text{ }-9[/tex]Let's find a, use f(-2) = 0.
[tex]f\mleft(-2\mright)=0[/tex][tex]\text{ 0 = a\lbrack(-2) - 1\rbrack}^2\text{ - 9}[/tex][tex]\text{ 0 = a(-2 - 1)}^2\text{ - 9}[/tex][tex]\text{ 0 + 9 = a(-3)}^2\text{ - 9 + 9}[/tex][tex]\text{ 9 = 9a}[/tex][tex]\text{ }\frac{\text{9}}{9}\text{ = }\frac{\text{9a}}{9}[/tex][tex]\text{ a = 1}[/tex]Let's now complete the equation.
[tex]\text{ f(x) = a(x - 1)}^2\text{ }-9[/tex][tex]\text{ f(x) = (1)(x - 1)}^2\text{ }-9\text{ = (x - 1)}^2\text{ }-9\text{ }[/tex][tex]\text{ f(x) = x}^2\text{ - 2x + 1 - 9}[/tex][tex]\text{ f(x) = x}^2\text{ - 2x - 8}[/tex]Therefore, the answer is letter A.
Need help with logarithms please, will leave a good rating
Answers
Given the logarithm:
[tex]x=\log_922=\frac{\log_922}{\log_99}[/tex]Now, from the change-of-base property:
[tex]\frac{\log_922}{\log_99}=\frac{\ln22}{\ln9}[/tex]Finally:
[tex]x=\frac{\ln22}{\ln9}\approx1.407[/tex]The Cookie Factory wants to sell chocolate chip and peanut butter cookies in combination packages of 6-12cookies. At least three of each type of cookie should be in each package. The cost of making a chocolatechip cookie is 19 cents, and the selling price is 44 cents each. The cost of making a peanut butter cookie is13 cents, and the selling price is 39 cents. How many of each type of cookie should be in each package tomaximize the profit?A. 3 chocolate chip and 3 peanut butter B. 3 chocolate chip and 9 peanut butterC. 9 chocolate chip and 3 peanut butter D. 0 chocolate chip and 12 peanut butter
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Let the number of chocolate chip cookies sold=x
Let the number of peanut butter cookie sold =y
The cost of making a chocolate chip cookie is 19 cents, and the selling price is 44 cents each.
Therefore, the profit made on chocolate chip cookie
=44-19
=25 cents
=$0.25
The cost of making a peanut butter cookie is 13 cents, and the selling price is 39 cents.
Therefore, the profit made on peanut butter cookie
=39-13
=26 cents
=$0.26
Therefore, the profit made when x cookies and y cookies are sold will be:
P(x,y)=0.25x+0.26y
To determine how many of each type of cookie should be in each package to maximize the profit, we use the coordinates of the feasible region (which are given in the options).
Option A: x=3, y=3
P(x,y)=0.25(3)+0.26(3)=$1.53
Option B: x=3, y=9
P(x,y)=0.25(3)+0.26(9)=$3.09
Option C: x=9, y=3
P(x,y)=0.25(9)+0.26(3)=$3.03
Option D: x=0, y=12
P(x,y)=0.25(0)+0.26(12)=$3.12
Since the point (0,12) gives the highest value, 0 chocolate chip and 12 peanut butter cookies should be in each package to maximize the profit.
Transform BC according to (x,y) (x-4, y-1). Sketch and write coordinates for B'C.
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The coordinates of B are:
B = (-1 , -1)
And the coordinates of C are:
C = (-6 , 2)
Using the transformation:
B' = (-1 - 4, -1 - 1) = (-5, -2)
C' = (-6 - 4, 2 - 1) = (-10 , 1)
Please help me by telling me the correct order please this is for my study guide
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Okay, here we have this:
Considering the provided information, we are going to organize the steps correctly, so we obtain the following:
Step 1. Isolate the term with variables on one side of the equation and arrange them in descending order.
Step 2. Divide by the coefficient of squared term if that coefficient is not 1.
Step 3. Complete the square by taking half of the 1st degree term and adding its square.
Step 4. Express one side of the equation as the square of binomial.
Step 5. Use the principle of square root.
Step 6. Solve for the variable.
Find one positive and one negative angle coterminal with an angle of 166°. 1) 526°, –194°2) 516°, –14°3) 526°, –764) 256°, –76°
Answers
SOLUTION
A coterminal angle is an angle that points to an exact direction like the original angle.
Since a complete circle is 360 degrees.
The positive coterminal angle will be
[tex]360^0+166^0=526^0[/tex]Hence the positive coterminal angle is 526°
Then the negative coterminal angle will be
[tex]166^0-360^0=-194^0[/tex]hence the negative coterminal angle will be -194°
The positive and negative coterminal angle to 166° are 526°, -194°
Therefore the right option is 1(A)
Graph the following function on a coordinate graph.take a number (x), quadruple it , and subtract 2.
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First, we have to write the function in the form:
y= mx+b
take a number x. quadruple it (multiply by 4) and subtract 2:
4x-2
So, the function is:
y=4x-2
The graph crosses the y-axis at y=-2 ( y-intercept) and has a slope of 4
Calculate the sum of the first 8 terms of the arithmetic sequence in which a8=-1 and the common difference is d=-8
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In the arithmetic sequence, the nth term is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
n is the position of the number
Since a(8) = -1
Then n = 8
Since the common difference is -8, then
d = -8
Substitute them in the rule to find the first term a
[tex]\begin{gathered} -1=a+(8-1)(-8) \\ -1=a+(7)(-8) \\ -1=a-56 \end{gathered}[/tex]Add 56 to each side
[tex]\begin{gathered} -1+56=a-56+56 \\ 55=a \end{gathered}[/tex]The first term is 55
The rule of the sum of the nth term is
[tex]S_n=\frac{n}{2}\lbrack a+l\rbrack[/tex]l is the last term
Since we need the sum of 8 terms, then
a = 55
l = a(8) = -1
n = 8
[tex]\begin{gathered} S_8=\frac{8}{2}\lbrack55+(-1)\rbrack \\ S_8=4\lbrack54\rbrack \\ S_8=216 \end{gathered}[/tex]The sum of the first 8 terms is 216
The answer is A
The points D(4,−5)(4,−5), E(4,0)(4,0), F(−5,2)(−5,2), and G(−5,−3)(−5,−3) form parallelogram DEFG. Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter of the parallelogram. Round your answer to the nearest tenth if necessary.
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The coordinates of the parallelogram are given to be:
[tex]\begin{gathered} D=\left(4,-5\right) \\ E=\left(4,0\right) \\ F=\left(-5,2\right) \\ G=\left(-5,-3\right) \end{gathered}[/tex]The graph is shown below:
To get the perimeter of the shape, the lengths of the lines are to be calculated.
According to the property of a parallelogram, the opposite sides are equal. Therefore:
[tex]\begin{gathered} EF=DG \\ FG=ED \end{gathered}[/tex]The length of line ED can be calculated to be:
[tex]ED=0-(-5)=5\text{ units}[/tex]The length of line EF can be calculated using the distance formula:
[tex]\begin{gathered} EF=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \therefore \\ EF=\sqrt{(-5-4)^2+(2-0)^2} \\ EF=\sqrt{81+4} \\ EF=\sqrt{85} \end{gathered}[/tex]Therefore, the perimeter is calculated as follows:
[tex]Perimeter=2(5)+2(\sqrt{85})=28.4[/tex]ANSWER
[tex]Perimeter=28.4\text{ units}[/tex]Circle R has a diameter ST with endpoints at S(4,5) and T (-2,-3).
Answers
Given
[tex]\begin{gathered} S(4,5) \\ T(-2,-3) \end{gathered}[/tex]Solution
Diameter is 10
Radius is 5
The Circumference
[tex]\begin{gathered} =2\pi r \\ \\ =2\times\pi\times5 \\ =10\pi \\ =31.42 \\ \end{gathered}[/tex]The area of the circle
[tex]\begin{gathered} =\pi r^2 \\ =\pi\times5^2 \\ =25\pi \\ =78.54 \end{gathered}[/tex]The length of a rectagular swimming pool is 50 feet. The width of the pool is 20 feet. What is the length of the diagonal of the pool ?
Answers
The schematic below represents the rectangle,
Note that the diagonal forms the hypotenuse of the triangle with base 50 ft and height 20 ft.
So the length of diagonal can be obtained using Pythagoras Theorem as follows,
[tex]\begin{gathered} \text{Hypotenuse}^2=\text{Base}^2+\text{height}^2 \\ \text{Hypotenuse}^2=\text{50}^2+\text{2}0^2 \\ \text{Hypotenuse}^2=\text{2500}+400 \\ \text{Hypotenuse}^2=\text{2}900 \\ \text{Hypotenuse}=\sqrt[]{2900} \\ \text{Hypotenuse}\approx53.85 \end{gathered}[/tex]Thus, the length of the diagonal of the pool is 53.85 approximately.
Since third option is closest to the answer, third option will be the correct choice.
Hi, can you help me answer this question please, thank you
Answers
First, find the degrees of freedom.
[tex]df=n-1=53-1=52[/tex]The t-value of 52 degrees of freedom is 2.01.
Then, we use the following formula.
[tex]\bar{x}\pm t\cdot\frac{s}{\sqrt[]{n}}=71.6\pm2.01\cdot\frac{16.6}{\sqrt[]{53}}=71.6\pm4.6[/tex]Therefore, the confidence interval is
[tex]67\leq\mu\leq76.2[/tex]Answer:
Step-by-step explanation:
What is the distance between the following points?Y4+ + ++++ 21 2 3 4 5 6 7 8 9-3-4-5-6-7-8
Answers
Distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]You have the points with coordinates (x,y):
(2,-3) and (8,-9)
[tex]undefined[/tex]the trashcan to clear all your answers.Factor completely, then place the factors in the proper location on the grid.13y2 - 5yx - 8x2
Answers
Answer:
[tex](-8x-13y)(x-y)[/tex]Step-by-step explanation:
To factor the following expression:
[tex]\begin{gathered} 13y^2-5yx-8x^2 \\ -8x^2-5xy+13y^2 \\ (-8x-13y)(x-y) \end{gathered}[/tex]