To multiply this expression we can use this rule:
(a - b)^2 = a^2 - 2ab + b^2(a−b)2=a2−2ab+b2
If we let: a = 4m^2a=4m2 and b = 2nb=2n and substitute we get:
(4m^2 - 2n)^2 = (4m^2)^2 - 2(4m^2)(2n) + (2n)^2 =(4m2−2n)2=(4m2)2−2(4m2)(2n)+(2n)2=
16m^4 - 16m^2n + 4n^216m4−16m2n+4n2
Another way to multiply this is to first rewrite the expression as:
(4m^2 - 2n)(4m^2 - 2n)(4m2−2n)(4m2−2n)
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))(4m2−2n)(4m2−2n) 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))(4m2×4m2)−(4m2×2n)−(2n×4m2)+(2n×2n)
16m^4 - 8m^2n - 8m^2n + 4n^216m4−8m2n−8m2n+4n2
We can now combine like terms:
16m^4 + (-8 - 8)m^2n + 4n^216m4+(−8−8)m2n+4n2
16m^4 + (-16)m^2n + 4n^216m4+(−16)m2n+4n2
16m^4 - 16m^2n + 4n^216m4−16m2n+4n2
