1. ## Factoring Problem Help

Hello,

I need help on factoring the following expression...

2x^2 + 4xy + 2y^2 + 5x - 3 + 5y

(x + y + 3)(2x + 2y - 1)...

However, I can't figure out the proper steps that was used in between...
Can anyone help?
Thank you!

2. Hello, student101!

This is a tricky one . . .

factor: .$\displaystyle 2x^2 + 4xy + 2y^2 + 5x - 3 + 5y$

Answer: .$\displaystyle (x + y + 3)(2x + 2y - 1)$

We have: .$\displaystyle \left(2x^2 + 4xy + 2y^2\right) + \left(5x + 5y \right) - 3$

. . . . . .$\displaystyle =\;2(x^2 + 2xy + y^2) + 5(x+y) - 3$

. . . . . .$\displaystyle =\;2(x+y)^2 + 5(x+y) - 3$

. . . . . .$\displaystyle =\;\bigg[(x+y)+3\bigg]\,\bigg[2(x+y) - 1\bigg]$

. . . . . .$\displaystyle =\; (x+y+3)(2x + 2y - 1)$

3. What have you tried? What do you think has to be done?

I would suggest re-arranging this expression first,

Originally Posted by student101

2x^2 + 4xy + 2y^2 + 5x - 3 + 5y

4. 2x^2 + 4xy + 2y^2 + 5x - 3 + 5y

$\displaystyle x^2 + 2xy + y^2 + \frac{5(x+y)}{2} - \frac{3}{2}$

$\displaystyle (x+y)^2 + 2\frac{5}{4}(x+y)} + (\frac{5}{4})^2 - (\frac{5}{4})^2 - \frac{3}{2}$

$\displaystyle (x+y+\frac{5}{4})^2 - (\frac{7}{4})^2$

Now proceed.

5. Hello soroban,

Thank you for the step-by-step solution...I never expected it to be that simple...
I did not see that (x+y) could be considered as a single term...Now I know! Thank you once again