How do you factor the expression $- 5 a^{2} - a b + 6 b^{2}$ $-5a^2 - ab + 6b^2$ ?

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How do you factor the expression $- 5 a^{2} - a b + 6 b^{2}$ $-5a^2 - ab + 6b^2$ ?

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Answer 1 · 2017-07-04T20:11:13

$(5 a + 6 b) (b - a)$ $(5a+6b)(b-a)$

Explanation:

If you multiply the coefficients of $a^{2} and b^{2}$ $a^2 and b^2$ you get $- 30$ $-30$ . You need factors of $- 30$ $-30$ which differ by $- 1$ $-1$ , namely $- 6$ $-6$ and 5 which allows you to rewrite the equation as:

$- 5 a^{2} - 6 a b + 5 a b + 6 b^{2}$ $-5a^2-6ab+5ab+6b^2$

You can factorize both pairs separately to give you:

$- a (5 a + 6 b) + b (5 a + 6 b)$ $-a(5a+6b) + b(5a+6b)$ which you collect as the answer above

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How do you factor the expression $- 5 a^{2} - a b + 6 b^{2}$ $-5a^2 - ab + 6b^2$ ?

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How do you factor the expression $- 5 a^{2} - a b + 6 b^{2}$ $-5a^2 - ab + 6b^2$ ?