# How do you multiply ( x + 7 ) ( x − 4 ) ( x − 7 ) ( x − 4 ) ?

Apr 4, 2018

$2 {x}^{2} - 8 x - 33$

Here's how I did it:

#### Explanation:

$\left(x + 7\right) \left(x - 4\right) \left(x - 7\right) \left(x - 4\right)$

It's easier to solve it when we look at it like this instead:
$\left(x + 7\right) \left(x - 7\right) \left(x - 4\right) \left(x - 4\right)$

First, let's do the $\left(x + 7\right) \left(x - 7\right)$ part:
$x \cdot x = {x}^{2}$

$x \cdot - 7 = - 7 x$

$7 \cdot x = 7 x$

$7 \cdot - 7 = - 49$

When we combine it all together, we get:
${x}^{2} - 7 x + 7 x - 49$

And we can simplify that to get:
${x}^{2} - 49$

Now let's do the $\left(x - 4\right) \left(x - 4\right)$ part:
$x \cdot x = {x}^{2}$

$x \cdot - 4 = - 4 x$

$- 4 \cdot x = - 4 x$

$- 4 \cdot - 4 = 16$

When we combine it all together, we get:
${x}^{2} - 4 x - 4 x + 16$

And we can simplify that to get:
${x}^{2} - 8 x + 16$

And when we combine everything together, we get:
${x}^{2} - 49 + {x}^{2} - 8 x + 16$

We can simplify this to get:
$2 {x}^{2} - 8 x - 33$

Hope this helps!