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. $- 6 x ( 3 - 6 x ) ( 3 + 6 x )$
A) $- 18 x + 216 x ^ { 3 }$
B) $- 18 x + 36 x ^ { 3 }$
C) $- 54 x + 216 x ^ { 3 }$
D) $- 54 x + 36 x ^ { 3 }$
E) $- 54 x - 216 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The product $(3 - 6x)(3 + 6x)$ fits the pattern $(a - b)(a + b) = a^2 - b^2$, where $a = 3$ and $b = 6x$. Thus, the product simplifies to $3^2 - (6x)^2 = 9 - 36x^2$. Multiplying this by $-6x$ gives $-6x \cdot 9 + (-6x) \cdot (-36x^2) = -54x + 216x^3$.

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