Question

Factorice 16(a-2b)^2-(a+b)^2 leaving your answer in the simplest form

Answer 1

Factor is a verb. Or, you can say factorize (no doubt, factorise in Britain), but never factorice.

16(a-2b)^2 - (a+b)^2 is the difference of two squares, so its factors are

(4(a-2b)+(a+b))(4(a-2b)-(a+b))
= (4a-8b+a+b)(4a-8b-a-b)
= (5a-7b)(3a-9b)
= 3(5a-7b)(a-3b)