Question

What is the answer to [(x²+4x)-2]²

Answer 1

`x^(4)` + 8x³ + 12x² - 16x + 4

Explanation:

Given

[(x² + 4x) - 2 ]² ← simplify contents of bracket

= (x² + 4x - 2)² = (x² + 4x - 2)(x² + 4x - 2)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(x² + 4x - 2) + 4x(x² + 4x - 2) - 2(x² + 4x - 2) ← distribute parenthesis

=
`x^(4)` + 4x³ - 2x² + 4x³ + 16x² - 8x - 2x² - 8x + 4 ← collect like terms

=
`x^(4)` + 8x³ + 12x² - 16x + 4