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#