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

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Answer 1 · 2018-04-11T08:18:00

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

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

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

$= m^4 + 4m^3p - p^2m^2 - 4m^3p - 16m^2p^2 + 4mp^3 + p^2m^2 + 4mp^3 - p^4$

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

Answer 2 · 2018-04-11T08:41:27

$(m^2 - 4mp + p^2)(m^2 + 4mp - p^2)=m^4-16m^p^2+8mp^3-p^4$

One can use formula $(a-b)(a+b)=a^2-b^2$ as follows:

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

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

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

= $m^4-(16m^2p^2-8mp^3+p^4)$

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

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