Question

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


PLEASE HELPPPPP!

Answer 1

(x^2-11x+28)(6-x-x^2)2x^2 - 12x + 34

Answer 2

-10x +34

Explanation:

$(x-4)(x-7)$

(x-4)(x-7) &= x(x-7) - 4(x-7)\\

&=x^2 - 7x -4x +28\\

&=x^2 - 11x + 28.

$(3-x)(2+x)$

(3-x)(2+x) &= 3(2+x) - x(2+x)\\

&=6 + 3x - 2x - x^2\\

&= 6+x -x^2.

(x-4)(x-7) + (3-x)(2+x) &= (x^2 - 11x + 28) + (6+x-x^2)\\

&= (x^2 - x^2) + (-11x + x) + (28 + 6)\\

=-10x + 34