1. ## Factoring

I have this advanced grade 11 factoring question $\displaystyle y^4+2y^2+9$ and i know the answer is $\displaystyle (y^2+3-2y)(y^2+3-2y)$ however I do not know how to get there because when i first factored it i got $\displaystyle y^2(y+1)(y-1)+9$ which is wrong. Any help or tricks are appreciated!

2. ## Re: Factoring

$\displaystyle y^2+2y^2+9=3y^2+9=3(y^2+3)$

3. ## Re: Factoring

sorry i wrote down the wrong question.

4. ## Re: Factoring

Hello, sakonpure6!

The answer you gave is wrong . . .

$\displaystyle \text{Factor: }\:y^4+2y^2+9$

We have: .$\displaystyle y^4 + 9 + 2y^2$

Add and subtract $\displaystyle 6y^2:$

. . $\displaystyle y^4 {\color{red}\:+\: 6y^2} + 9 + 2y^2 {\color{red}\:-\: 6y^2} \;=\;(y^4 + 6y^2 + 9) - 4y^2$

. . . . . $\displaystyle =\;(y^2+ 3)^2 - (2y)^2$ . . . a difference of squares!

Factor: .$\displaystyle \big[(y^2+3) - 2y\big]\,\big[(y^2+3) + 2y\big] \;=\;(y^2 - 2y + 3)(y^2 + 2y +3)$

5. ## Re: Factoring

why did you choose to add 6y^2? can it be something else as long as we get a perfect square trinomial or...?

6. ## Re: Factoring

it's a algebra solving trick, I learn it in my 12th grade, where I learnt more techniques and procedures of trigonometry and other problem solving phenomenon. Most of problem and Solving Linear Equations With Fractions are also solved by using adding and subtracting.

7. ## Re: Factoring

thank you but i still do not understand how Soroban came up with $\displaystyle 6y^2$ to add and subtract