Question

Which of the following is the correct factorization of the polynomial below?
27x^3 + 64y^3
A. (4x + 3y)(2x+8y)
O B. (4x + 3y)(9x2 - 12xy + 16y2)
C. (3x + 4y)(9x2 - 12xy + 16y2)
D. The polynomial is irreducible.

Answer 1

Answer option C

27x³+64y³

it's written as

(3x)³ +(4y)³

Now by using identify

a³+b³=(a+b)(a²-ab+b²)

(3x)³+(4y)³= (3x+4y){(3x)² - 3x*4y+(4y)²}

→ (3x+4y)( 9x²-12xy+16y²)

So required answer is option C