Question

Factorise (a+2b)(3a+b)-(a+b)(a+2b)+(a+2b)^2

Answer 1

Answer:

Step-by-step explanation:

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

=(3a^2+ab+6ab+2b^2)-(a^2+2ab+ab+2b^2)+(a^2+4ab+4b^2)

=(3a^2+7ab+2b^2)-(a^2+3ab+2b^2)+(a^2+4ab+4b^2)

=3a^2+7ab+2b^2-a^2-3ab-2b^2+a^2+4ab+4b^2

=3a^2-a^2+a^2+a^2+7ab-3ab+4ab+2b^2-2b^2+4b^2

=3a^2+8ab+4b^2

=3a^2+5ab+2ab+4b^2

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

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

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