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

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Answer 1 · 2015-11-20T15:31:31

$y=3x^3-x+2$

Given $(color(blue)(x^2-1))(3x-1) + (color(red)(x+1))(x+1)$

$y= color(blue)(x^2)(3x-1) color(blue)(-1)(3x-1)color(red)(+x)(x+1)color(red)(+1)(x+1)$

$y=(3x^3-x^2)+(-3x+1)+(x^2+x)+(x+1)$

Collecting like terms

$y= 3x^3 +(-x^2+x^2)+(-3x+x+x)+(1+1)$

$y=3x^2+0-x+2$

$y=3x^3-x+2$

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