What is the complete factorization of 5y^2-45y^6 ?

Question

My teacher told me that 5y^2(1-9y^4) was not the correct answer and I was wondering what it was and I have not yet been able to figure it out.

Answer 1

 

5y² - 45y⁶ = 5y² ( 1⁴ - 9y⁴ ) = 5y² (1² + 3y²) (1² - 3y²) = 5y² (1 + 3y² ) (1 + √3 y) (1 - √3 y)

 

Your teacher was right! He/She wanted you to completely factorize the given expression, not to stop in the middle of the process. Words in Math are critical!

Answer 2

You did good except you needed to continue by applying the difference of squares law which says:

 

If you have two squares with a minus sign between them, they can be factored into the difference of the squares times the sum of the squares. 

In your problem, this means:

 

1-9y^4  = ( 1 - 3y^2 ) ( 1 + 3y^2 )