Question

Which of the following is equivalent to (a-2)(a^2+2a+4)?

A. a(a-2)(a-2)
B. a(a+2)(a-2)
C. a^3+8
D. a^3-8

Answer 1

To expand (a-2)(a^2+2a+4), distribute the first term, a, to each term inside the second parentheses. Simplify and combine like terms to get a^3 - 8 as the equivalent expression.

Step-by-step explanation:

To expand the expression (a-2)(a^2+2a+4), we can use the distributive property. We will distribute the first term, a, to each term inside the second parentheses.

This gives us a(a^2) + a(2a) + a(4) - 2(a^2) - 2(2a) - 2(4).

Simplifying further, we get a^3 + 2a^2 + 4a - 2a^2 - 4a - 8.

Combining like terms, we have a^3 - 8 as the equivalent expression.