# How do you multiply (m^2-4mp+p^2)(m^2+4mp-p^2) ?

Apr 11, 2018

Please look below(I hope I got the algebra right).

#### Explanation:

$\left({m}^{2} - 4 m p + {p}^{2}\right) \left({m}^{2} + 4 m p - {p}^{2}\right)$

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

$= {m}^{4} + 4 {m}^{3} p - {p}^{2} {m}^{2} - 4 {m}^{3} p - 16 {m}^{2} {p}^{2} + 4 m {p}^{3} + {p}^{2} {m}^{2} + 4 m {p}^{3} - {p}^{4}$

$= {m}^{4} - 16 {m}^{2} {p}^{2} + 8 m {p}^{3} - {p}^{4}$

Apr 11, 2018

$\left({m}^{2} - 4 m p + {p}^{2}\right) \left({m}^{2} + 4 m p - {p}^{2}\right) = {m}^{4} - 16 {m}^{p} ^ 2 + 8 m {p}^{3} - {p}^{4}$

#### Explanation:

One can use formula $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$ as follows:

$\left({m}^{2} - 4 m p + {p}^{2}\right) \left({m}^{2} + 4 m p - {p}^{2}\right)$

= (m^2 - (4mp - p^2))((m^2 + (4mp - p^2))

= ${\left({m}^{2}\right)}^{2} - {\left(4 m p - {p}^{2}\right)}^{2}$

= ${m}^{4} - \left(16 {m}^{2} {p}^{2} - 8 m {p}^{3} + {p}^{4}\right)$

= ${m}^{4} - 16 {m}^{2} {p}^{2} + 8 m {p}^{3} - {p}^{4}$