How do you multiply ${(x - 4 y)}^{2}$ $(x-4y)^2$ ?

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How do you multiply ${(x - 4 y)}^{2}$ $(x-4y)^2$ ?

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Answer 1 · 2017-01-16T03:30:29

See entire solution process below:

Explanation:

First, we convert this expression to:

${(x - 4 y)}^{2} = (x - 4 y) (x - 4 y)$ $(x - 4y)^2 = (x - 4y)(x - 4y)$

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

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

$(x \times x) - (x \times 4 y) - (4 y \times x) + (4 y \times 4 y)$ $(color(red)(x) xx color(blue)(x)) - (color(red)(x) xx color(blue)(4y)) - (color(red)(4y) xx color(blue)(x)) + (color(red)(4y) xx color(blue)(4y))$

$x^{2} - 4 x y - 4 x y + 16 y^{2}$ $x^2 - 4xy - 4xy + 16y^2$

We can now combine like terms:

$x^{2} + (- 4 - 4) x y + 16 y^{2}$ $x^2 + (-4 - 4)xy + 16y^2$

$x^{2} - 8 x y + 16 y^{2}$ $x^2 - 8xy + 16y^2$

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How do you multiply ${(x - 4 y)}^{2}$ $(x-4y)^2$ ?

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