Simplify the expression $(x-4)(x-7) + (3-x)(2+x).$

You made a small mistake in the second to the last expansion. It should be:

x^2 - 11 x + 28 + (3 - x) (x + 2)

-x^2 + x + 6 + x^2 - 11 x + 28

-10 x + (x^2 - x^2) + (28 + 6)

-10x + 34, or: 34 - 10x

Step by Step:

1. Write out expression

(x-4)(x-7) + (3-x)(2+x)

2. Expand

x^{2 }- 7x - 4x - 28 + (-)x^{2} - 2x + 3x + 6

3. Simplify for both sides around the '+'

x^{2} -11x - 28 + (-)x^{2} + x + 6

4. Simplify expression to get the answer.

-10x - 22