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

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Answer 1 · 2015-11-20T15:31:31

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

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

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

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

Collecting like terms

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

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

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

What is the standard form of y=(x2−1)(3x−1)+(x+1)2y= (x^2-1)(3x-1) + (x+1)^2?