Question

what is the factored form of $x^3 + 64$?$(x^2 + 8)(x + 8)LXB0(x - 4)(x^2 + 4x + 16)$done

Explanation:

Step1: Identify sum of cubes

$x^3 + 64 = x^3 + 4^3$

Step2: Apply sum of cubes formula

Recall $a^3+b^3=(a+b)(a^2-ab+b^2)$. Here $a=x$, $b=4$.

$$\begin{align*} x^3+4^3&=(x+4)(x^2 - x\cdot4 + 4^2)\\ &=(x+4)(x^2-4x+16) \end{align*}$$

Step3: Verify other options

• $(x^2+8)(x+8)=x^3+8x^2+8x+64

eq x^3+64$

• $(x-4)(x^2+4x+16)=x^3-64

eq x^3+64$

Answer:

$(x + 4)(x^2 - 4x + 16)$