How do you multiply $(x^3+5x^2-3x-2) (x^2-2x+1)$ ?

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Answer 1 · 2015-08-23T11:15:29

$=color(blue)(x^5+3x^4-12x^3+9x^2+x-2$

$color(blue)((x^2−2x+1)) * (x^3+5x^2−3x−2)$

$=color(blue)((x^2)) * (x^3+5x^2−3x−2) +color(blue)((-2x)) * (x^3+5x^2−3x−2) +color(blue)(1) * (x^3+5x^2−3x−2)$

$=x^5+5x^4-3x^3-2x^2color(blue)(-2x^4-10x^3+6x^2+4x)+x^3+5x^2−3x−2$

Adding like terms

$=color(blue)(x^5+3x^4-12x^3+9x^2+x-2$

How do you multiply (x^3+5x^2-3x-2) (x^2-2x+1)(x^3+5x^2-3x-2) (x^2-2x+1)?