# How do you simplify (x + y)(x - y)?

Jul 22, 2016

$\left(x + y\right) \left(x - y\right) = {x}^{2} - {y}^{2}$

#### Explanation:

To simplify $\left(x + y\right) \left(x - y\right)$ we use distributive property of number systems.

Let us treat $\left(x + y\right)$ as a single number and distribute it over $\left(x - y\right)$.

This makes $\left(x + y\right) \left(x - y\right)$

= $\left(x + y\right) x - \left(x + y\right) y$

Now using commutative property of multiplication the above is equivalent to

$x \left(x + y\right) - y \left(x + y\right)$ and now again using distributive property this is equivalent to

$x \times x + x \times y - y \times x - y \times y$

$x \times x + x \times y - x \times y - y \times y$

= ${x}^{2} + x y - x y - {y}^{2}$

= ${x}^{2} + \cancel{x y} - \cancel{x y} - {y}^{2}$

= ${x}^{2} - {y}^{2}$