Completely factor the expression. $$3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$$
A) $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$
B) $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$
C) $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$
D) $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$
E)prime

Question

Quizplus · Accepted Answer

First factor out the common factor of $3$.  $$3( a ^ { 2 } x ^ { 2 } + 4 a ^ { 2 } x + 4 a ^ { 2 } - 2 b ^ { 2 } x ^ { 2 } - 8 b ^ { 2 } x - 8 b ^ { 2 })$$Next, group the first three terms and the last three terms and factor each of the two groups.  $$3a^2(x^2+4x+4)-6b^2(x^2+4x+4)$$$$=(x+2)^2(3a^2-6b^2)$$$$=3(x+2)^2(a^2-2b^2)$$Therefore, the answer is $\boxed{\mathrm{(D)}}$.

Completely Factor the Expression 3a2x2+12a2x+12a2−6b2x2−24b2x−24b23 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }3a2x2+12a2x+12a2−6b2x2−24b2x−24b2

Completely Factor the Expression $3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$