Question

question 14 of 25
how would the expression $x^3 - 64$ be rewritten using difference of cubes?

a. $(x + 4)(x^2 - 4x - 16)$
b. $(x - 4)(x^2 + 4x + 16)$
c. $(x + 4)(x^2 - 4x + 16)$
d. $(x - 4)(x^2 + 16x + 4)$

Explanation:

Step1: Recall difference of cubes formula

The formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.

Step2: Identify a and b in the expression

$x^3 - 64 = x^3 - 4^3$, so $a = x$, $b = 4$.

Step3: Substitute into the formula

Substitute $a=x$, $b=4$: $(x - 4)(x^2 + x\cdot4 + 4^2) = (x - 4)(x^2 + 4x + 16)$.

Answer:

B. (x - 4)(x² + 4x + 16)