Question

Simplify:
(x² − 3x + 2)(5x − 2) − (3x² + 4x − 5)(2x − 1)

Answer 1

To simplify, we will  proceed as follows:

$$(x^2-3x+2)(5x-2)-(3x^2+4x-5)(2x-1)$$

$$=\left[(x^2-3x+2)(5x-2)\right]-\left[(3x^2+4x-5)(2x-1)\right]$$

$$=[5x(x^2-3x+2)-2(x^2-3x+2)]-[2x(3x^2+4x-5)-1\times (3x^2+4x-5)]$$          (Distributive law)

$$=[5x^3-15x^2+10x-(2x^2-6x+4)]-[6x^3+8x^2-10x-3x^2-4x+5]$$

$$=[5x^3-15x^2+10x-2x^2+6x-4]-[6x^3+8x^2-10x-3x^2-4x+5]$$

$$=5x^3-15x^2+10x-2x^2+6x-4-6x^3-8x^2+10x+3x^2+4x-5$$

$$=5x^3-6x^3-15x^2-2x^2-8x^2+3x^2+10x+6x+10x+4x-5-4$$    (Rearranging)

$$=-x^3-22x^2+30x-9$$         (Combining like terms)

Thus, the answer is $$-x^3-22x^2+30x-9$$.