Question

question 4 of 10
factor the expression given below. write each factor as a polynomial in
descending order. enter exponents using the caret (^). for example, you
would enter ( x^2 ) as x^2.
( 125x^3 + 343y^3 )

Explanation:

Step1: Identify the formula for sum of cubes

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). Here, \(125x^3=(5x)^3\) and \(343y^3=(7y)^3\), so \(a = 5x\) and \(b = 7y\).

Step2: Apply the sum of cubes formula

Substitute \(a = 5x\) and \(b = 7y\) into the formula:
\((5x)^3+(7y)^3=(5x + 7y)((5x)^2-(5x)(7y)+(7y)^2)\)

Step3: Simplify each part

Simplify \((5x)^2 = 25x^2\), \((5x)(7y)=35xy\), and \((7y)^2 = 49y^2\). So the factored form is \((5x + 7y)(25x^2 - 35xy + 49y^2)\).

Answer:

\((5x + 7y)(25x^2 - 35xy + 49y^2)\)