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

Question

4697 views around the world

You can reuse this answer
Creative Commons License

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.)

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