Question

multiply to find the expand form of each product (a b)^2 (a b)^3 (a b)^4

Answer 1

(a + b)^2 = (a + b)(a + b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2

(a + b)^3 = (a + b)(a + b)(a + b) = (a + b)(a^2 + 2ab + b^2) = a^3 + 2a^2 b + ab^2 + a^2 b + 2ab^2 + b^3 = a^3 + 3a^2 b + 3ab^2 + b^3

(a + b)^4 = (a + b)(a + b)(a + b)(a + b) = (a + b)(a^3 + 3a^2 b + 3ab^2 + b^3) = a^4 + 3a^3 b + 3a^2 b^2 + ab^3 + a^3 b + 3a^2 b^2 + 3ab^3 + b^4 = a^4 + 4a^3 b + 6a^2 b^2 + 4ab^3 + b^4