Use one of the appropriate patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$ $( a - b ) ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$ $( a + b ) ( a - b ) = a ^ { 2 } - b ^ { 2 }$ to find the following product. $( 6 x + 7 y ) ^ { 2 }$
A) $36 x ^ { 2 } + 84 x y + 7 y ^ { 2 }$
B) $36 x ^ { 2 } - 84 x y + 49 y ^ { 2 }$
C) $36 x ^ { 2 } + 42 x y + 49 y ^ { 2 }$
D) $36 x ^ { 2 } + 84 x y + 49 y ^ { 2 }$
E) $36 x ^ { 2 } + 49 y ^ { 2 }$

Question

Quizplus · Accepted Answer

Using the pattern $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$, we can expand $(6x+7y)^2$ as 
\begin{align*}
(6x+7y)^2 &= (6x)^2 + 2(6x)(7y) + (7y)^2 \
&= 36x^2 + 84xy + 49y^2
\end{align*}
Therefore, the answer is choice D.

Use One of the Appropriate Patterns (a+b)2=a2+2ab+b2( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }(a+b)2=a2+2ab+b2

Use One of the Appropriate Patterns $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$