Question

(3ab+b)^2-(3a-b)^2 divided by 3ab help pleaseeee

Answer 1

3ab + 2b + 2 - (3a)/b

Explanation:

first, multiply out brackets of both 3ab + b and 3a - b.

(3ab + b)² = 9a²b² + 3ab² + 3ab² + b²

= 9a²b² + 6ab² + b².

(3a - b)² = 9a² - 3ab - 3ab + b² = 9a² - 6ab + b².

(3ab+b)²- (3a-b)²

= (9a²b² + 6ab² + b²) - (9a² - 6ab + b²)

= 9a²b² + 6ab² - 9a² + 6ab

= 9a²b² + 6ab² + 6ab - 9a².

there's clearly factors of 3, a, b. so, factorise.

3ab (3ab + 2b + 2) - 9a².

now we can divide by 3ab:

[3ab (3ab + 2b + 2) - 9a²] / 3ab

= [3ab (3ab + 2b + 2)] / 3ab - (9a²)/3ab

= 3ab + 2b + 2 - (3a)/b