Question

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

Answer 1

Step-by-step explanation:

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

=a^2+4ab+4b^2-(4a^2-4ab+b^2)

=a^2+4ab+4b^2-4a^2+4ab-b^2

=-3a^2+8ab+3b^2

=-3a^2+9ab-ab+3b^2

=-3a(a-3b)-b(a-3b)

=(a-3b)(-3a-b)

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

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