Factor 5m^2n+5mp^2+n^2p^2+mn^3

$5 m^{2} n + 5 m p^{2} + n^{2} p^{2} + m n^{3}$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 m^{2} n + 5 m p^{2}) + n^{2} p^{2} + m n^{3}$

Factor out the greatest common factor (GCF) from each group.

$5 m (p^{2} + m n) + n^{2} (p^{2} + m n)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $p^{2} + m n$ .

$(p^{2} + m n) (5 m + n^{2})$