How do you expand #(m+2n)^4#?

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Answer 1 · 2017-04-21T16:21:55

#m^4 + 8m^3n + 24m^2n^2 + 32mn^3 + 16n^4#

#m^4 + 4m^3(2n) + 6m^2(2n)^2 + 4m(2n)^3 + (2n)^4#

Answer 2 · 2017-04-21T16:50:40

#=m^4+ 8m^3n +24m^2n^2 +32mn^3 +16n^4#

To reduce the amount of steps required I would regard this as the product of 2 trinomials.

#(m+2n)^4#

#=(m+2n)^2 xx(m+2n)^2#

#=(color(red)(m^2)+color(blue)(4mn) +color(green)(4n^2)) xx (m^2+4mn +4n^2)#

#= color(red)(m^4+4m^3 n +4m^2n^2) + color(blue)(4m^3n +16m^2n^2 +16mn^3)+color(green)(4m^2n^2 +16mn^3 +16n^4) #

#=m^4+ 8m^3n +24m^2n^2 +32mn^3 +16n^4#

(This can also be done using the binomial expansion.)