Question

NEED ASAP PLEASE
You are given the expression 40x4y3 − 25x3y.

Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable. (1 point)

Part B: Explain how you found the common factor. (1 point)

Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work. (2 points)

Answer 1

Given expression

• 40x⁴y³ - 25x³y

Part A

The common factor is:

• 5x³y

Part B

Find the prime factors of both terms and find the common part:

• 40x⁴y³ = 2³*5x⁴y⁵
• 25x³y = 5²*x³y

Common part is 5x³y

Part C

• 40x⁴y³ - 25x³y  =
• 5x³y(8xy² - 5)

Answer 2

Answer:

$\textsf{A.} \quad 5x^3y$

B.   Both terms of the given expression are made up of a constant, an x variable and a y variable.  To find the common factor of the expression, find the highest common factor of these three components.

$\textsf{C.} \quad 5x^3y(8xy^2-5)$

Step-by-step explanation:

Given expression:

$40x^4y^3-25x^3y$

Both terms of the given expression are made up of a constant, an x variable and a y variable.  

To find the common factor of the given expression, find the highest common factor of these three components:

• The highest common factor of 40 and 25 is 5.  
• The highest common factor of x⁴ and x³ is x³.
• The highest common factor of the y³ and y is y.

Therefore, the common factor is 5x³y.

To rewrite the expression using the common factor, rewrite 40 as 8·5 and 25 as 5·5:

$\implies 8\cdot 5 x^{(3+1)}y^{(1+2)}-5\cdot5x^3y$

Rewrite the exponent of x⁴ as (3+1) and the exponent of y³ as (1+2):

$\implies 8\cdot 5x^{(3+1)}y^{(1+2)}-5\cdot5x^3y$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:$

$\implies 8\cdot 5x^3xyy^2-5\cdot5x^3y$

Rearrange:

$\implies 8xy^2\cdot 5x^3y-5\cdot5x^3y$

Factor out the common term 5x³y:

$\implies 5x^3y(8xy^2-5)$