Question

Simplify the expression and find its value: (2x+0.5)^2–(2x–0.5)^2 for x=−3.5

Simplified expression is
. For x = −3.5, the value of the expression is
.

Answer 1

-14

Explanation:

(2x+0.5)^2–(2x–0.5)^2 for x=−3.5

By far the easiest way in which to approach this evaluation is to treat 2x+0.5 as a+b and 2x-0.5 as a-b.

Then a^2 + 2ab + b^2 - [a^2 - 2ab + b^2] = 4ab. Returning to 2x+0.5 = a+b, we see that ab = x.

We found that (a+b)^2 - (a-b)^2 = 4ab. But we also found that ab = x. Thus, 4ab = 4x.

Replacing x with -3.5, we get 4(-3.5) = -14 (answer)