Question

PLZ HELP ASAP!!!!
expand the polynomials and simplify:
(1/4m-2n)^2

Answer 1

1/16m^2 -2*1/4m*2n+4n^2

If you want to write it in more simple picture :

1/16m^2 -mn +4n^2

Answer 2

`\left((1)/(4)m-2n\right)^2=(m^2)/(16)-mn+4n^2`

Explanation:

Given the polynomial

`\left((1)/(4)m-2n\right)^2`

Expanding and simplifying

`\left((1)/(4)m-2n\right)^2`

as 1/4 = 4/m, so

`=\left((m)/(4)-2n\right)^2`

Apply perfect square formula:
`\left(a-b\right)^2=a^2-2ab+b^2`

`=\left((m)/(4)\right)^2-2\cdot (m)/(4)\cdot \:2n+\left(2n\right)^2`

simplifying

`=(m^2)/(4^2)-mn+2^2n^2`

`=(m^2)/(16)-mn+4n^2`

Therefore,

`\left((1)/(4)m-2n\right)^2=(m^2)/(16)-mn+4n^2`