9(a+b)^2-(a-b)^2

how would you factor that?

9(a^2+2ab+b^2)-(a^2-2ab+b^2)

=8a^2+16ab+8b^2
=8a^2+8ab+8ab+8b^2
=8a(a+b)+8b(a+b)
=8(a+b)(a+b)
=8(a+b)^2

recognize the difference of squares

= ( 3(a+b) + (a-b) (3(a+b) - (a-b) )
= (4a + 2b)(2a + 4b)
= 4(2a+b)(a+2b)

check:
let a = 2 , b = 1
original:
= 9(3)^2 - 1^2
= 80

mine:
= 4(5)(4) = 80

deepali's :
= 8(3^2) = 72 ≠ 80

deepali's answer is not correct.

To factor the expression 9(a+b)^2 - (a-b)^2, we can follow these steps:

Step 1: Expand the expression
Expand (a+b)^2 and (a-b)^2 using the rule (a+b)^2 = a^2 + 2ab + b^2, and (a-b)^2 = a^2 - 2ab + b^2.

9(a+b)^2 - (a-b)^2 = 9(a^2 + 2ab + b^2) - (a^2 - 2ab + b^2)

Step 2: Distribute the coefficients
Distribute the coefficient 9 across the terms in (a^2 + 2ab + b^2):

= 9a^2 + 18ab + 9b^2 - (a^2 - 2ab + b^2)

Step 3: Combine like terms
Combine the terms with the same variables:

= 9a^2 + 18ab + 9b^2 - a^2 + 2ab - b^2

Step 4: Simplify the expression
Simplify the expression by adding or subtracting the coefficients:

= 8a^2 + 20ab + 8b^2

Now, the expression 9(a+b)^2 - (a-b)^2 is factored as 8a^2 + 20ab + 8b^2