To multiply this expression we can use this rule:
#(a - b)^2 = a^2 - 2ab + b^2#
If we let: #a = 4m^2# and #b = 2n# and substitute we get:
#(4m^2 - 2n)^2 = (4m^2)^2 - 2(4m^2)(2n) + (2n)^2 =#
#16m^4 - 16m^2n + 4n^2#
Another way to multiply this is to first rewrite the expression as:
#(4m^2 - 2n)(4m^2 - 2n)#
Then, to multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
#(color(red)(4m^2) - color(red)(2n))(color(blue)(4m^2) - color(blue)(2n))# becomes:
#(color(red)(4m^2) xx color(blue)(4m^2)) - (color(red)(4m^2) xx color(blue)(2n)) - (color(red)(2n) xx color(blue)(4m^2)) + (color(red)(2n) xx color(blue)(2n))#
#16m^4 - 8m^2n - 8m^2n + 4n^2#
We can now combine like terms:
#16m^4 + (-8 - 8)m^2n + 4n^2#
#16m^4 + (-16)m^2n + 4n^2#
#16m^4 - 16m^2n + 4n^2#
