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

2 Answers
Apr 30, 2018

Answer:

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

Explanation:

Simplify:

#(3x-3)(x-5)#

Use the FOIL method:

https://formulas.tutorvista.com/math/foil-formula.html

#(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#

Apr 30, 2018

Answer:

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#