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

1 Answer
Kevin B. · Lewis
Nov 12, 2016

It depends what you mean by simplified:
Factored Form: #(x-6)(x-2)(x-3)#
Expanded Form: #x^3-11x^2+36x-36#

Explanation:

"Simplified" depends on what you are asking for. I am placing both interpretations in the answer box for reference.

The Factored Form was what you gave in the problem.

The Expanded Form is what you get by distributing out all the terms; this is commonly referred to as the FOIL method.

#(x-6)(x-2)(x-3)#

Take two of the factors and distribute them.
#(x^2-6x-2x+12)(x-3)#
#(x^2-8x+12)(x-3)#

Now distribute the third factor:
#[x(x^2-8x+12)-3(x^2-8x+12)]#
#x^3-8x^2+12x-3x^2+24x+36#
#x^3-11x^2+36x-36#

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