(x-5)(x+2)-(x-7)(x+4)

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To expand the expression:

First, distribute (x-5)(x+2):

(x)(x) + (x)(2) + (-5)(x) + (-5)(2)
= x^2 + 2x - 5x - 10
= x^2 - 3x - 10

Next, distribute -(x-7)(x+4):

(-x)(x) + (-x)(4) + (-7)(x) + (-7)(4)
= -x^2 - 4x - 7x - 28
= -x^2 - 11x - 28

Now, subtract the second expression from the first:

(x^2 - 3x - 10) - (-x^2 - 11x - 28)
= x^2 - 3x - 10 + x^2 + 11x + 28
= 2x^2 + 8x + 18

Therefore, the expanded expression is 2x^2 + 8x + 18.