# How do you multiply (x + y + 3)(x + y - 4)?

Aug 25, 2016

The Expression$= {x}^{2} + 2 x y + {y}^{2} - x - y - 12$.

#### Explanation:

Letting $x + y = z$, we find that,

The Expression$= \left(z + 3\right) \left(z - 4\right) = z \left(z - 4\right) + 3 \left(z - 4\right) = {z}^{2} - 4 z + 3 z - 12$

$= {z}^{2} - z - 12$

Surrendering $z = x + y$, we get,

The Expression$= {\left(x + y\right)}^{2} - x - y - 12$

$= {x}^{2} + 2 x y + {y}^{2} - x - y - 12$.