# How do you factor 4p^2q+pq^2+4p^3 by grouping?

Jun 21, 2016

$4 {p}^{2} q + p {q}^{2} + 4 {p}^{3} = p \left(q + 2 p\right) \left(q + 2 p\right)$

#### Explanation:

Separate out the common factor $p$, rearrange into descending powers of $q$ then recognise the perfect square trinomial:

$4 {p}^{2} q + p {q}^{2} + 4 {p}^{3}$

$= p \left(4 p q + {q}^{2} + 4 {p}^{2}\right)$

$= p \left({q}^{2} + 4 p q + 4 {p}^{2}\right)$

$= p \left(q + 2 p\right) \left(q + 2 p\right)$