# How do you simplify (3x - 3)(x - 5)?

Apr 30, 2018

$\left(3 x - 3\right) \left(x - 5\right) = 3 {x}^{2} - 18 x + 15$

#### Explanation:

Simplify:

$\left(3 x - 3\right) \left(x - 5\right)$

Use the FOIL method:

$\left(3 x - 3\right) \left(x - 5\right) = \left(3 x\right) \left(x\right) + \left(3 x\right) \left(- 5\right) + \left(- 3\right) \left(x\right) + \left(- 3\right) \left(- 5\right)$

Simplify.

$\left(3 x - 3\right) \left(x - 5\right) = 3 {x}^{2} - 15 x - 3 x + 15$

Collect like terms.

$\left(3 x - 3\right) \left(x - 5\right) = 3 {x}^{2} + \left(- 15 x - 3 x\right) + 15$

Simplify.

$\left(3 x - 3\right) \left(x - 5\right) = 3 {x}^{2} - 18 x + 15$

Apr 30, 2018

Using the FOIL method, we find that $\left(3 x - 3\right) \left(x - 5\right) = 3 {x}^{2} - 18 x + 15$

#### Explanation:

To simplify a problem like this, we use the FOIL method: First, Outside, Inside, Last.

For example, in the equation $\left(a + b\right) \left(c + d\right)$, the FOIL method begins like this:

First: We multiply the two "first" values, a and c
Outside: We multiply the outside values, a and d
Inside: We multiply the inside values, b and c
Last: We multiply the two "last" values, b and d

So for $\left(3 x - 3\right) \left(x - 5\right)$, the FOIL method begins like this:

First: We multiply the two "first" values, 3x and x
Outside: We multiply the outside values, 3x and -5
Inside: We multiply the inside values, -3 and x
Last: We multiply the two "last" values, -3 and -5

Now we simply add each of these together. So in our first example, we would have $a c + a d + b c + b d$.

In the problem we're trying to solve, we get $\left(3 {x}^{2}\right) + \left(- 15 x\right) + \left(- 3 x\right) + \left(15\right)$

We finish simplifying by combining like terms, so in this example -15x and -3x can be added to get -18x. Remember, we only add terms with the same variable.

So the final simplified answer is $3 {x}^{2} - 18 x + 15$