Answer:
[tex]x^{4}[/tex] + 8x³ + 12x² - 16x + 4
Step-by-step 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
= [tex]x^{4}[/tex] + 4x³ - 2x² + 4x³ + 16x² - 8x - 2x² - 8x + 4 ← collect like terms
= [tex]x^{4}[/tex] + 8x³ + 12x² - 16x + 4
