How do you multiply (4m^2-2n)^2?

1 Answer
smendyka
Apr 24, 2017

See the solution process below:

Explanation:

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

Related questions
See all questions in Special Products of Polynomials
Impact of this question
2732 views around the world
You can reuse this answer
Creative Commons License