Question

Write as a polynomial (a+2b)(4a–5b)–(3a–b)(b–a)

Answer 1

7a^2-ab-9b^2

Explanation:

Let's do this in two steps. First, we multiply the first two parentheses:

(a+2b)(4a-5b)

4a^2-5ab+8ab-10b^2 = 4a^2+3ab-10b^2

Then, do the other two parentheses:

(3a-b)(b-a)

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

Then, combine them:

4a^2+3ab-10b^2-4ab+3a^2+b^2 = 7a^2-ab-9b^2