Question

9(a+b)^2-(a-b)^2
how would you factor that?

Answer 1

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

Answer 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.