How do you factor the expressions $x^{2} - x y - 2 y^{2}$ $x^2-xy-2y^2$ ?

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How do you factor the expressions $x^{2} - x y - 2 y^{2}$ $x^2-xy-2y^2$ ?

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Answer 1 · 2016-03-05T20:45:38

$(x + y) (x - 2 y)$ $(x+y)(x-2y)$

Explanation:

Look for a factor pair of the product of the coefficients of the first and last terms $1 \times - 2 = - 2$ $1xx-2=-2$ whose sum is the coefficient of the middle term, $- 1$ $-1$ . The factors that work are $- 2$ $-2$ and $1$ $1$ .

Split up $- x y$ $-xy$ into $- 2 x y$ $-2xy$ and $+ x y$ $+xy$ (their coefficients are the two factors we just found, $- 2$ $-2$ and $1$ $1$ ) and then factor by grouping.

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

$= x (x - 2 y) + y (x - 2 y)$ $=x(x-2y)+y(x-2y)$

$= (x + y) (x - 2 y)$ $=(x+y)(x-2y)$

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How do you factor the expressions $x^{2} - x y - 2 y^{2}$ $x^2-xy-2y^2$ ?

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How do you factor the expressions $x^{2} - x y - 2 y^{2}$ $x^2-xy-2y^2$ ?