Question

which expression shows the complete factored form of $x^3 + 27$?
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 the 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 \(x^3+27\)

In the expression \(x^3 + 27\), we can write \(x^3+27=x^3 + 3^3\). So, \(a = x\) and \(b=3\).

Step3: Apply the sum of cubes formula

Substitute \(a = x\) and \(b = 3\) into the sum of cubes formula \((a + b)(a^2 - ab + b^2)\). We get \((x + 3)(x^2-3x + 9)\).

Answer:

C. \((x + 3)(x^2 - 3x + 9)\)