Question

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

Answer 1

Answer:

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

Answer:

$\left(\frac{1}{4}m-2n\right)^2=\frac{m^2}{16}-mn+4n^2$

Step-by-step explanation:

Given the polynomial

$\left(\frac{1}{4}m-2n\right)^2$

Expanding and simplifying

$\left(\frac{1}{4}m-2n\right)^2$

as 1/4 = 4/m, so

$=\left(\frac{m}{4}-2n\right)^2$

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

$=\left(\frac{m}{4}\right)^2-2\cdot \frac{m}{4}\cdot \:2n+\left(2n\right)^2$

simplifying

$=\frac{m^2}{4^2}-mn+2^2n^2$

$=\frac{m^2}{16}-mn+4n^2$

Therefore,

$\left(\frac{1}{4}m-2n\right)^2=\frac{m^2}{16}-mn+4n^2$