## AngelaB97 one year ago how do you factorize x^4+27x

1. zepdrix

Hey Angela! They've both got some x's... factor those out first.$\large\rm x^4+27x=x(x^3+27)$From there you want to utilize your Sum of Cubes Formula: $$\large\rm a^3+b^3=(a+b)(a^2-ab+b^2)$$

2. zepdrix

Hmm but we only have one thing being cubed... x. If you can find a way to rewrite 27 as a perfect cube, you can apply this formula!

3. AngelaB97

but how do you get (a+b)(a^2-ab+b^2) from x(x^3+27)? @zepdrix

4. zepdrix

You get $$\large\rm (a+b)(a^2-ab+b^2)$$ from $$\large\rm a^3+b^3$$ and you get $$\large\rm a^3+b^3$$ from $$\large\rm x^3+27$$

5. zepdrix

the x^3 matches up with the a^3, it's in the correct format. But we need to rewrite 27 as $$\large\rm something^3$$

6. zepdrix

Example: $$\large\rm 8=2\cdot2\cdot2$$ therefore $$\large\rm 8=2^3$$ We found a way to write 8 as a perfect cube! Can you find a way to do that with 27?

7. AngelaB97

thank you!