Not sure what this is called.

**Lucy1** · July 16th 2009, 12:29 AM

I am not sure what this type of equation is called, but anyway this is the formula

(3x+2y)^2 – (x-y)^2
4x + 6y

And the answer is =2x + y/2

So i know i have to factor out the numerator but for the life of me i cannot see how they come up with that answer, can anyone please explain how this works?

Much appreciated.

p.s what this type of equation called?

**yeongil** · July 16th 2009, 12:42 AM

Originally Posted by Lucy1

I am not sure what this type of equation is called, but anyway this is the formula

(3x+2y)^2 – (x-y)^2
4x + 6y

And the answer is =2x + y/2

So i know i have to factor out the numerator but for the life of me i cannot see how they come up with that answer, can anyone please explain how this works?

Much appreciated.

p.s what this type of equation called?

I'd call this a rational expression.

The numerator is a difference of two squares:
$a^2 - b^2 = (a + b)(a - b)$

In our case, a = 3x + 2y and b = x - y, so
$\frac{(3x + 2y)^2 - (x - y)^2}{4x + 6y}$
$\begin{aligned} &= \frac{[(3x + 2y) + (x - y)][(3x + 2y) - (x - y)]}{2(2x + 3y)} \\ &= \frac{(4x + y)(2x + 3y)}{2(2x + 3y)} \\ &= \frac{4x + y}{2} \\ &= \frac{4x}{2} + \frac{y}{2} \\ &= 2x + \frac{y}{2} \\ \end{aligned}$

01

**red_dog** · July 16th 2009, 12:42 AM

Use the formula $a^2-b^2=(a-b)(a+b)$

$(3x+2y)^2-(x-y)^2=[(3x+2y)-(x-y)][(3x+2y)+(x-y)]$

Can you continue?

**Lucy1** · July 16th 2009, 12:54 AM

yip i understand that , thanks alot, now i can attempt some other examples.

Thanks!!

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