Use a special product pattern to find the product $\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)$ .

A) $81 x ^ { 2 } - 64$
B) $81 x ^ { 2 } - 72 x + 64$
C) $81 x ^ { 4 } - 144 x ^ { 2 } + 64$
D) $81 x ^ { 4 } - 17 x ^ { 2 } - 64$
E) $81 x ^ { 4 } - 64$

Question

Use a special product pattern to find the product

\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)

.

A)

81 x ^ { 2 } - 64

B)

81 x ^ { 2 } - 72 x + 64

C)

81 x ^ { 4 } - 144 x ^ { 2 } + 64

D)

81 x ^ { 4 } - 17 x ^ { 2 } - 64

E)

81 x ^ { 4 } - 64

Karina Molina · Accepted Answer

Final Answer : E, Explanation :   The given expression is an example of the difference of squares formula,  a^2 - b^2 = (a + b)(a - b) , where  a = 9x^2  and  b = 8 . Therefore, the product is  81x^4 - 64 .

Use a special product pattern to find the product $\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)$ .

A) $81 x ^ { 2 } - 64$
B) $81 x ^ { 2 } - 72 x + 64$
C) $81 x ^ { 4 } - 144 x ^ { 2 } + 64$
D) $81 x ^ { 4 } - 17 x ^ { 2 } - 64$
E) $81 x ^ { 4 } - 64$

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