Question

question 2 of 10
how would the expression ( x^3 + 27 ) be rewritten using sum of cubes?

a. ( (x + 3)(x^2 - 3x + 9) )
b. ( (x + 3)(x^2 + 3x - 9) )
c. ( (x - 3)(x^2 - 3x + 9) )
d. ( (x + 3)(x^2 - 3x - 9) )

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 in the expression

For $x^3 + 27$, $a = x$ (since $x^3 = x^3$) and $b = 3$ (since $27 = 3^3$).

Step3: Substitute into the formula

Substitute $a = x$ and $b = 3$: $(x + 3)(x^2 - (x)(3) + 3^2) = (x + 3)(x^2 - 3x + 9)$.

Answer:

A. $(x + 3)(x^2 - 3x + 9)$