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

2 Answers
Oct 21, 2017

Answer:

#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

Answer:

#(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#