How do you factor by grouping $15b^2-22bc-5c^2$ ?

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Answer 1 · 2015-05-03T07:05:19

To solve this using Grouping, we need 4 terms.

We can split the middle term of this expression to get 4 terms

We need to think of 2 numbers such that:

$N_1*N_2 = 15*-5 = -75$
AND
$N_1 +N_2 = -22$

After trying out a few numbers we get $N_1 = -25$ and $N_2 =3$

$-25*3 = -75$ , and $-25+3= -22$

We write the expression as:

$15b^2-25bc+3bc-5c^2$

We make Groups of two terms:

$=(15b^2-25bc)+(3bc-5c^2)$

$= 5b(3b - 5c) + c(3b - 5c)$

$3b-5c$ is a Common Factor to each of the terms

$= color(green)((3b-5c)(5b+c)$

How do you factor by grouping 15b^2-22bc-5c^215b^2-22bc-5c^2?