How do you multiply #(x-4y)^2#?

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Answer 1 · 2017-01-16T03:30:29

See entire solution process below:

First, we convert this expression to:

#(x - 4y)^2 = (x - 4y)(x - 4y)#

Now, to multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(x) - color(red)(4y))(color(blue)(x) - color(blue)(4y))# becomes:

#(color(red)(x) xx color(blue)(x)) - (color(red)(x) xx color(blue)(4y)) - (color(red)(4y) xx color(blue)(x)) + (color(red)(4y) xx color(blue)(4y))#

#x^2 - 4xy - 4xy + 16y^2#

We can now combine like terms:

#x^2 + (-4 - 4)xy + 16y^2#

#x^2 - 8xy + 16y^2#