Question #73265

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Answer 1 · 2017-06-01T21:00:01

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

Treat this like a quadratic of the form $ax^2+bx+c$ .

$a=2$
$b=y$
$c=-y^2$

Now, to factor, we need to find 2 factors of $ac$ which add up to $b$ .

$ac = 2(-y^2) = -2y^2$

We can use $2y$ and $-y$ , since $2y(-y)=-2y^2$ and $2y+(-y)=y$ . This satisfies both conditions of multiplying to make $ac$ and adding up to $b$ .

Our factored form will look like this:

$a(x+"factor 1"/a)(x+"factor 2"/a)$

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

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

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

Final Answer