Question

Factor completely.



m4 - n4



(m2- n2)(m + n)(m - n) ****
(m2+ n2)(m + n)(m - n)
(m2+ n2)(m - n)2
I think it is *******

Answer 1

It would be the second one. m^4-n^4 could factor to become (m^2+n^2)(m^2-n^2). To further factor it, you change (m^2-n^2) to (m+n)(m-n). So the answer is (m^2+n^2)(m+n)(m-n). Then check your work

First multiply the last two to become m^2-nm+nm-n^2, which simplifies to m^2-n^2. Then multiply that by (m^2+n^2) which would be \[m ^{4}+m^2n^2-m^2n^2+n^4\] Which can be simplified by combining like terms to \[m^4+n^4\]The answer is the second one.