How do you factor the expression $- 2 a^{2} - a b + 3 b^{2}$ $-2a^2-ab+3b^2$ ?

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How do you factor the expression $- 2 a^{2} - a b + 3 b^{2}$ $-2a^2-ab+3b^2$ ?

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Answer 1 · 2016-03-24T13:55:19

$- (a - b) (2 a + 3 b)$ $-(a-b)(2a+3b)$

Explanation:

$- 2 a^{2} - a b + 3 b^{2}$ $−2a^2−ab+3b^2$ => Factor out -1:
$= - (2 a^{2} + a b - 3 b^{2})$ $=-(2a^2+ab-3b^2)$
Write the 2nd term as factors of 1st and last term i.e:
$a b = - 2 a b + 3 a b$ $ab=-2ab+3ab$ => We get:
$= - (2 a^{2} - 2 a b + 3 a b - 3 b^{2})$ $=-(2a^2-2ab+3ab-3b^2)$ => Factor by grouping:
$= - [2 a (a - b) + 3 b (a - b)]$ $=-[2a(a-b)+3b(a-b)]$ => Finally:
$= - (a - b) (2 a + 3 b)$ $=-(a-b)(2a+3b)$

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How do you factor the expression $- 2 a^{2} - a b + 3 b^{2}$ $-2a^2-ab+3b^2$ ?

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Explanation:

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