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

the answer is -70.25

Answer 2

The simplified expression is 4(x + 0.5)(x - 0.5), and its value for x = -3.5 is 64.

Step-by-step explanation:

Expand the squares:

(2x + 0.5)^2 = 4x^2 + 2x + 0.25

(2x - 0.5)^2 = 4x^2 - 2x + 0.25

Difference of squares:

Subtract the second expression from the first:

(2x + 0.5)^2 - (2x - 0.5)^2 = (4x^2 + 2x + 0.25) - (4x^2 - 2x + 0.25)

This simplifies to:

4x^2 + 2x + 0.25 - 4x^2 + 2x - 0.25 = 4x

Factoring out the common factor 4, we get:

4x = 4(x + 0.5)

Evaluate for x = -3.5:

Substitute x = -3.5 into the simplified expression:

4(-3.5 + 0.5) = 4(-3) = -12

However, the original expression had the squares of (2x + 0.5) and (2x - 0.5). Each square inherently has a positive value. Therefore, the correct answer is:

4(x + 0.5)(x - 0.5)

Evaluating this expression with x = -3.5:

4(-3.5 + 0.5)(-3.5 - 0.5) = 4(-3)(-4) = 48 + 16 = 64

Therefore, the simplified expression is 4(x + 0.5)(x - 0.5), and its value for x = -3.5 is 64.