Question

factor by grouping; u^4 + u^2 - v^2 - v^4

Answer 1

\[\large u^4+u^2-v^2-v^4\]



\[\large u^4-v^4+u^2-v^2\]




\[\large (u^2-v^2)(u^2+v^2)+(u-v)(u+v)\]



\[\large (u-v)(u+v)(u^2+v^2)+(u-v)(u+v)\]



\[\large (u-v)(u+v)(u^2+v^2+1)\]

So \[\large u^4+u^2-v^2-v^4=(u-v)(u+v)(u^2+v^2+1)\]