Question

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

Answer 1

`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`

Answer 2

`(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`