How do you multiply $(x + y)(x + y)$ ?

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Answer 1 · 2017-03-17T22:11:37

See a couple of solution processes below:

This is an example of the perfect square. The formula for this is:

$(a + b)(a + b) = a^2 + 2ab + b^2$

Substituting $x$ for $a$ and $y$ for $b$ gives:

$(x + y)(x + y) = x^2 + 2xy + y^2$

Another way to show this is the correct answer is as follows:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$(color(red)(x) + color(red)(y))(color(blue)(x) + color(blue)(y))$ becomes:

$(color(red)(x) xx color(blue)(x)) + (color(red)(x) xx color(blue)(y)) + (color(red)(y) xx color(blue)(x)) + (color(red)(y) xx color(blue)(y))$

$x^2 + xy + xy + y^2$

We can now combine like terms:

$x^2 + 1xy + 1xy + y^2$

$x^2 + (1 + 1)xy + y^2$

$x^2 + 2xy + y^2$

How do you multiply (x + y)(x + y)(x + y)(x + y)?