Question

1. (a + b)(a³ - 3ab - b²)

Explanation:

Step1: Distribute $a$ to each term

$a(a^3 - 3ab - b^2) = a^4 - 3a^2b - ab^2$

Step2: Distribute $b$ to each term

$b(a^3 - 3ab - b^2) = a^3b - 3ab^2 - b^3$

Step3: Combine all resulting terms

$a^4 - 3a^2b - ab^2 + a^3b - 3ab^2 - b^3$

Step4: Combine like terms

$a^4 + a^3b - 3a^2b + (-ab^2 - 3ab^2) - b^3 = a^4 + a^3b - 3a^2b - 4ab^2 - b^3$

Answer:

$a^4 + a^3b - 3a^2b - 4ab^2 - b^3$