Question

which of the following is the correct factorization of the polynomial below? 8x³ + 27y³
a. (4x + 3y)(2x + 9y)
b. (2x + 3y)(4x² - 6xy + 9y²)
c. (4x + 3y)(2x² - 2xy + 9y²)
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: Rewrite the given polynomial

We have $8x^{3}+27y^{3}=(2x)^{3}+(3y)^{3}$, where $a = 2x$ and $b = 3y$.

Step3: Apply the sum - of - cubes formula

Substituting $a = 2x$ and $b = 3y$ into the formula, we get $(2x)^{3}+(3y)^{3}=(2x + 3y)[(2x)^{2}-(2x)(3y)+(3y)^{2}]=(2x + 3y)(4x^{2}-6xy + 9y^{2})$.

Answer:

B. $(2x + 3y)(4x^{2}-6xy + 9y^{2})$