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

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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