How do you simplify (x-3)(2x-5)-(x+1)(x-6)?

2 Answers
Oct 21, 2017

x^2-6x+21

Explanation:

You can expend the expression.

(x-3)(2x-5)-(x+1)(x-6)

=(x)(2x)+(x)(-5)-3(2x)-3(-5)-[(x)(x)+(x)(-6)+1(x)+1(-6)]

=2x^2-5x-6x+15-(x^2-6x+x-6)
=2x^2-11x+15-x^2+5x+6
=x^2-6x+21

Oct 21, 2017

(x-3)(2x-5) - (x+1)(x-6) = x^2-6x+21

Explanation:

(x-3)(2x-5) - (x+1)(x-6)

Use the distributive law to expand both equations:
(a+b)*(c+d)= (ac + ad + bc + bd)

=((x*2x)+(x*-5)+(-3*2x)+(-3*-5)) - ((x*x)+(x*-6)+(1*x)+(1*-6))
=(2x^2 -5x-6x+15) - (x^2-6x+x-6)
=(2x^2-11x+15)-(x^2-5x-6)
=2x^2-11x+15-x^2+5x+6
=x^2-6x+21

Therefore:
(x-3)(2x-5) - (x+1)(x-6) = x^2-6x+21