Question

factorise: a(a+b)^2 - 2ab(a+b)

Answer 1

=(a+b){ a(a+b)-2ab}
= (a+b){a²+ab-2ab}
= (a+b){a²-ab}
=(a+b){a(a-b)}
= (a+b)a(a-b)

Answer 2

$a(a+b)^2-2ab(a+b)\\ \\ =[a+b] \times [a(a+b)-2ab]\\ \\ =[a+b] \times [a^2+ab-2ab]\\ \\ =[a+b] \times [a^2-ab]\\ \\ =[a+b] \times [a(a-b)]\\ \\=a(a+b)(a-b)$