Question

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

Answer 1

`(3x-3)(x-5)=3x^2-18x+15`

Explanation:

Simplify:

`(3x-3)(x-5)`

Use the FOIL method:

`(3x-3)(x-5)=(3x)(x) + (3x)(-5) + (-3)(x) + (-3)(-5)`

Simplify.

`(3x-3)(x-5)=3x^2-15x-3x+15`

Collect like terms.

`(3x-3)(x-5)=3x^2 + (-15x-3x) +15`

Simplify.

`(3x-3)(x-5)=3x^2-18x+15`

Answer 2

Using the FOIL method, we find that `(3x-3)(x-5)=3x^2-18x+15`

Explanation:

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

For example, in the equation `(a+b)(c+d)`, 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 `(3x-3)(x-5)`, 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 `ac+ad+bc+bd`.

In the problem we're trying to solve, we get `(3x^2)+(-15x)+(-3x)+(15)`

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 `3x^2-18x+15`