[tex]Use\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\x^3+8=x^3+2^3=(x+2)(x^2+2x+2^2)\\\\=\boxed{(x-2)(x^2+2x+4)}[/tex]
Answer:
(x + 2)(x² – 2x + 4)
Step-by-step explanation:
To determine if this expression is equal to x³+8, use the distributive property:
x(x²)+x(-2x)+x(4)+2(x²)+2(-2x)+2(4)
x³-2x²+4x+2x²-4x+8
Rearranging this to group like terms together,
x³-2x²+2x²+4x-4x+8
Combining like terms, we see that
-2x²+2x² = 0
and
4x-4x = 0. This leaves us with
x³+8
