What is the standard form of y= (x-1)(2x-7)(3x-1)?

1 Answer
Nov 2, 2017

6x^3-29x^2+30x-7

Explanation:

To expand the polynomial we've been given, we'll need to repeatedly apply the distributive property as we go through each of the binomials. Since the bulk of the explanation here is calculation, I'll walk through and justify the steps here:

(x-1)(2x-7)(3x-1)=
#=(x-1)2x-(x-1)7(3x-1)# (distribute the binomial x-1 to the 2x and the 7)
=(2x^2-2x-7x+7)(3x-1) (distribute the 2x and the 7 to the x and the -1)
=(2x^2-9x+7)(3x-1)
=(2x^2-9x+7)3x-(2x^2-9x+7) (distribute the trinomial 2x^2-9x+7 to the 3x and the 1)
=2x^2(3x)-9x(3x)+7(3x)-2x^2+9x-7
=6x^3-27x^2+21x-2x^2+9x-7
=6x^3-29x^2+30x-7 (combine like terms)