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#