(x-h)2 - (x-h)2

Mathematics
(x-h)2 - (x-h)2

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Answer

(3 - x)(3x - 11)

Step 1: Recognize the difference of squares formula.

The expression is (x−4)2−(2x−7)2(x-4)^2 - (2x-7)^2

This matches a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b), where a=x−4a = x-4 and b=2x−7b = 2x-7.

Step 2: Compute a−ba - b.

a−b=(x−4)−(2x−7)a - b = (x-4) - (2x-7) =x−4−2x+7= x - 4 - 2x + 7 =x−2x−4+7= x - 2x - 4 + 7 =−x+3= -x + 3

Step 3: Compute a+ba + b.

a+b=(x−4)+(2x−7)a + b = (x-4) + (2x-7) =x−4+2x−7= x - 4 + 2x - 7 =x+2x−4−7= x + 2x - 4 - 7 =3x−11= 3x - 11

Step 4: Write the factored form.

(x−4)2−(2x−7)2=(−x+3)(3x−11)(x-4)^2 - (2x-7)^2 = (-x + 3)(3x - 11)

Equivalently, (3−x)(3x−11)\boxed{(3 - x)(3x - 11)}

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