Question

simplify (2a+3b) (6a-2ab) - (a-b) (a+b)

Answer 1

Answer:

$(2a+3b) (6a-2ab) - (a-b) (a+b) = 11a^2 - 4a^2b + 18ab - 6ab^2 + b^2$

Step-by-step explanation:

Formula:

$(a +b) (a - b) = a^2 - b^ 2$

Given:

$(2a+3b) (6a-2ab) - (a-b) (a+b)\\= 2a (6a - 2ab) + 3b (6a - 2ab) - [a^2 - b^2]\\= (12a^2 - 4a^2b) + (18ab - 6ab^2) - [a^2 - b^2]\\= 12a^2 - 4a^2b + 18ab - 6ab^2 - a^2 + b^2$

Rearrange the similar terms

$= 12a^2 - a^2 - 4a^2b + 18ab - 6ab^2 + b^2\\= 11a^2 - 4a^2b + 18ab - 6ab^2 + b^2$