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. $( 3 x + 3 y ) ^ { 2 }$
A) $9 x ^ { 2 } + 18 x y + 3 y ^ { 2 }$
B) $9 x ^ { 2 } + 9 x y + 9 y ^ { 2 }$
C) $9 x ^ { 2 } + 18 x y + 9 y ^ { 2 }$
D) $9 x ^ { 2 } - 18 x y + 9 y ^ { 2 }$
E) none of these

Question

Quizplus · Accepted Answer

Using the pattern $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$, we have:

\begin{align*}
( 3 x + 3 y ) ^ { 2 } & = ( 3x ) ^ { 2 } + 2 ( 3x ) ( 3y ) + ( 3y ) ^ { 2 } \
& = 9 x ^ { 2 } + 18 x y + 9 y ^ { 2 }
\end{align*}

Therefore, the answer is choice C, $9 x ^ { 2 } + 18 x y + 9 y ^ { 2 }$.

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 $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$