How do you factorize these two questions: $X - y - x^{2} + y^{2}$ $X - y - x ^2+ y^2$ and $x^{3} - 36 x$ $x^3 - 36 x$ ?

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How do you factorize these two questions: $X - y - x^{2} + y^{2}$ $X - y - x ^2+ y^2$ and $x^{3} - 36 x$ $x^3 - 36 x$ ?

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Answer 1 · 2015-03-19T11:03:02

Watch the plusses and minuses!

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

$x^{3} - 36 x$ $x^3-36x$
$= x (x^{2} - 36)$ $=x(x^2-36)$
$= x (x - 6) (x + 6)$ $=x(x-6)(x+6)$

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How do you factorize these two questions: $X - y - x^{2} + y^{2}$ $X - y - x ^2+ y^2$ and $x^{3} - 36 x$ $x^3 - 36 x$ ?

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