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. $( x + 4 ) ^ { 2 }$
A) $x ^ { 2 } + 8 x + 16$
B) $x ^ { 2 } + 8 x + 4$
C) $x ^ { 2 } - 8 x + 16$
D) $x ^ { 2 } + 4 x + 16$
E) none of these

Question

Quizplus · Accepted Answer

Using the pattern $( a + b ) ^ { 2 } = a ^ { 2 } + 2 a b + b ^ { 2 }$, we have:
$$(x+4)^2 = x^2 + 2\cdot x\cdot 4 + 4^2 = x^2 + 8x + 16$$
Therefore, the best choice is A.

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