Help on factoring

[algebra1student]

Ive tried many steps with this problem but I have seem to not get a legit answer. Theres no GCF, you cant narrow things down after trying to factor.

Factor completely. If the polynomial cannot be factor, write prime.

16m^4 - 72m^2 + 81n^4

Thank you for you help guys

 

[soroban]

Hello, algebra1student!

I must assume that there is a typo . . .

\(\displaystyle \text{Factor completely: }\:16m^4 - 72m^2\color{red}{n^2} + 81n^4\)

\(\displaystyle 16m^4 - 72m^2n^2 + 81n^4\)

. . . \(\displaystyle =\;(4m^2 - 9n^2)^2\)

. . . \(\displaystyle =\;\big[(2m - 3n)(2m+3n)\big]^2 \)

. . . \(\displaystyle =\;(2m-3n)^2(2m+3n)^2\)

 

[algebra1student]

@Jeff- Sorry Im new here so I didnt know
@Soraban- Thank you very much!