Use a special product pattern to find the product $[ 9 u + ( v + 10 ) ] ^ { 2 }$ .
A) $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 180 u + 20 v + 100$
B) $81 u ^ { 2 } + v ^ { 2 } + 20 v + 100$
C) $81 u ^ { 2 } + v ^ { 2 } + 180 u + 20 v + 100$
D) $81 u ^ { 2 } + v ^ { 2 } + 100$
E) $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 20 v + 100$

Question

Quizplus · Accepted Answer

The correct expansion using the special product pattern $(a+b)^2 = a^2 + 2ab + b^2$ for $a = 9u$ and $b = v + 10$ gives $81u^2 + 2(9u)(v+10) + (v+10)^2$, which simplifies to $81u^2 + 18uv + 180u + v^2 + 20v + 100$.

Use a Special Product Pattern to Find the Product [9u+(v+10)]2[ 9 u + ( v + 10 ) ] ^ { 2 }[9u+(v+10)]2

Use a Special Product Pattern to Find the Product $[ 9 u + ( v + 10 ) ] ^ { 2 }$