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

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1 Answer
mason m
Nov 28, 2015

#y=x^3-4x^2+9x-10#

Explanation:

Calculate each part separately:

#(x-1)^3=overbrace((x-1)(x-1))^"multiply just these first"(x-1)#
#=(x^2-x-x+1)(x-1)#
#=(x^2-2x+1)(x-1)#
#=x^3-x^2-2x^2+2x+x-1#
#=x^3-3x^2+3x-1#

#(x-3)^2=(x-3)(x-3)#
#=x^2-3x-3x+9#
#=x^2-6x+9#

Put back into the original expression.

#y=(x^3-3x^2+3x-1)-(x^2-6x+9)#
#=color(red)(x^3)color(blue)(-3x^2)color(green)(+3x)color(purple)(-1)color(blue)(-x^2)color(green)(+6x)color(purple)(-9)#
#=x^3-4x^2+9x-10#

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