# Thread: Not sure what this is called.

1. ## Not sure what this is called.

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?

2. 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

3. 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?

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

Thanks!!