Use a special product pattern to find the product ( 7 x + 2 ) ( 7 x − 2 ) ( 7 x + 2 ) ( 7 x - 2 ) ( 7 x + 2 ) ( 7 x − 2 ) .A) 49 x 2 − 4 49 x ^ { 2 } - 4 49 x 2 − 4 B) 49 x 2 − 28 x + 4 49 x ^ { 2 } - 28 x + 4 49 x 2 − 28 x + 4 C) 49 x 2 + 4 49 x ^ { 2 } + 4 49 x 2 + 4 D) 49 x 2 − 9 x − 4 49 x ^ { 2 } - 9 x - 4 49 x 2 − 9 x − 4 E) 49 x 2 − 14 x + 4 49 x ^ { 2 } - 14 x + 4 49 x 2 − 14 x + 4

Question

Use a special product pattern to find the product   ( 7 x + 2 )  ( 7 x − 2 )  ( 7 x + 2 )  ( 7 x - 2 )  ( 7 x + 2 )  ( 7 x − 2 )    .A)    49 x 2 − 4 49 x ^ { 2 } - 4 49 x 2 − 4 B)    49 x 2 − 28 x + 4 49 x ^ { 2 } - 28 x + 4 49 x 2 − 28 x + 4 C)    49 x 2 + 4 49 x ^ { 2 } + 4 49 x 2 + 4 D)    49 x 2 − 9 x − 4 49 x ^ { 2 } - 9 x - 4 49 x 2 − 9 x − 4 E)    49 x 2 − 14 x + 4 49 x ^ { 2 } - 14 x + 4 49 x 2 − 14 x + 4

Omaima Othman · Accepted Answer

Final Answer : A, Explanation :   This is a special product pattern known as the difference of squares:   ( a + b ) ( a − b ) = a 2 − b 2 (a+b)(a-b) = a^2 - b^2 ( a + b ) ( a − b ) = a 2 − b 2  . In this case,   a = 7 x a = 7x a = 7 x   and   b = 2 b = 2 b = 2  , so we have   ( 7 x + 2 ) ( 7 x − 2 ) = ( 7 x ) 2 − ( 2 ) 2 = 49 x 2 − 4 (7x+2)(7x-2) = (7x)^2 - (2)^2 = 49x^2 - 4 ( 7 x + 2 ) ( 7 x − 2 ) = ( 7 x ) 2 − ( 2 ) 2 = 49 x 2 − 4  . Therefore, the best choice is A.

Use a special product pattern to find the product $(7 x + 2) (7 x - 2)$ .

A) $49 x ^ { 2 } - 4$
B) $49 x ^ { 2 } - 28 x + 4$
C) $49 x ^ { 2 } + 4$
D) $49 x ^ { 2 } - 9 x - 4$
E) $49 x ^ { 2 } - 14 x + 4$

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