Factor the polynomial by substitution.
-$$a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }$$
A) $( a - 9 b ) ( a + 8 b ) ( a + b )$
B) $( a + b ) ^ { 2 } ( a - 9 ) ( a + 8 )$
C) $( a + b ) ^ { 2 } ( a - 8 b ) ( a + 9 b )$
D) $( a + b ) ^ { 2 } ( a - 9 b ) ( a + 8 b )$

Question

Quizplus · Accepted Answer

First, factor out the common term $(a + b)^2$, resulting in $(a + b)^2 [a^2 - ab - 72b^2]$. Then, factor the quadratic expression inside the brackets as $(a - 9b)(a + 8b)$. Thus, the factored form is $(a + b)^2 (a - 9b)(a + 8b)$.

Factor the Polynomial by Substitution a2(a+b)2−ab(a+b)2−72b2(a+b)2a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }a2(a+b)2−ab(a+b)2−72b2(a+b)2

Factor the Polynomial by Substitution $a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }$