SOLUTION: how do I factor 4y^2+9z^4? I came up with the answer of 2y^2(2)+3z^4(3)

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Question 403240: how do I factor 4y^2+9z^4?
I came up with the answer of 2y^2(2)+3z^4(3)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
how do I factor 4y^2+9z^4?
That's the sum of two squares, since it can be written:

(2y)² + (3z²)²

Normally you can't factor the sum of two squares.  

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In rare cases you can but this time you can't.

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If your problem had been

y4 + 4z4

instead you could factor it by adding and subtracting 4y²z²

y4 + 4z4 + 4y²z² - 4y²z²

Rearranging terms:

y4 + 4y²z² + 4z4 - 4y²z²
 
(y4 + 4y²z² + 4z4) - 4y²z²

(y² + 2z²)² - 4y²z²

[(y² + 2z²) - 2yz][(y² + 2z²) + 2yz]

or

(y² - 2yz + 2z²)(y² + 2yz + 2z²)

But that's an advanced factoring technique, and will
not work on the problem you had without using square
roots.  So the answer to your problem is "It is a prime polynomial".

Edwin