Question

question 10 of 10
which of the following is the correct factorization of the polynomial below?
$8x^3 + 27y^3$

a. $(4x + 3y)(2x + 9y)$
b. $(2x + 3y)(4x^2 - 6xy + 9y^2)$
c. $(4x + 3y)(2x^2 - 2xy + 9y^2)$
d. the polynomial is irreducible.

Explanation:

Step1: Recall Sum of Cubes Formula

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\).

Step2: Identify \(a\) and \(b\)

For the polynomial \(8x^3+27y^3\), we can rewrite \(8x^3=(2x)^3\) and \(27y^3=(3y)^3\). So, \(a = 2x\) and \(b = 3y\).

Step3: Apply the Formula

Substitute \(a = 2x\) and \(b = 3y\) into the sum of cubes formula:
\((2x)^3+(3y)^3=(2x + 3y)((2x)^2-(2x)(3y)+(3y)^2)\)
Simplify the terms inside the second parenthesis:
\((2x)^2 = 4x^2\), \((2x)(3y)=6xy\), \((3y)^2 = 9y^2\). So we get \((2x + 3y)(4x^2-6xy + 9y^2)\).

Answer:

B. \((2x + 3y)(4x^2-6xy + 9y^2)\)