Factor the difference of two squares. $49 - 64 x ^ { 2 }$
A) $( 8 + 7 x ) ^ { 2 }$
B) $( 7 - 8 x ) ^ { 2 }$
C) $( 7 + 8 x ) ^ { 2 }$
D) $( 8 + 7 x ) ( 8 - 7 x )$
E) $( 7 + 8 x ) ( 7 - 8 x )$

Question

Quizplus · Accepted Answer

To factor the difference of two squares, we take the square root of both terms and put a plus sign in front of one square root and a minus sign in front of the other square root. In this case, we have 49 and 64x^2, which are perfect squares of 7 and 8x, respectively. So, we can write:

49 - 64x^2 = (7)^2 - (8x)^2

Then, using the formula for the difference of two squares, we get:

49 - 64x^2 = (7 + 8x)(7 - 8x)

Therefore, the answer is E.

Factor the Difference of Two Squares 49−64x249 - 64 x ^ { 2 }49−64x2

Factor the Difference of Two Squares $49 - 64 x ^ { 2 }$