How do you simplify #(3x - 3)(x - 5)#?
Use the FOIL method:
Collect like terms.
Using the FOIL method, we find that
To simplify a problem like this, we use the FOIL method: First, Outside, Inside, Last.
For example, in the equation
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
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
In the problem we're trying to solve, we get
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