How do you write #(x + 7)(x – 3)(x – 2)# in standard form?

1 Answer
ProfLayton
Apr 18, 2016

#=x^3+2x^2-29x+42#

Explanation:

This is a long one, but an easy one once you know this property: #(a+b)(c+d)=a(c+d)+b(c+d)=ab+ad+bc+bd#.
First lets ignore the #(x-2)#, and just expand the #(x+7)(x-3)#
#(x+7)(x-3)(x-2)=(x-2)*(x+7)(x-3)#

#=(x-2)*(x^2-3x+7x-21)#

#=(x-2)*(x^2+4x-21)#

#=x(x^2+4x-21)-2(x^2+4x-21)#

#=x^3+4x^2-21x-2x^2-8x+42#

#=x^3+2x^2-29x+42#

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