# Applying the distributive law...

#### tmy942

##### New member
I'm a beginner and I'm trying to wrap my head around some of the basics of algebra. So I have something like this...

y = 3 ( x + 5 ) ( x - 2 )

or this...

3(12-7r^2)(10r-5)

How would I apply the distributive law to these kinds of equations? I've been trying to research this but the only thing I can find is the distributive law in it's simplest form, i.e. a(b+c) = ab + ac. I already understand that. How would I apply it in situations with multiple sets of parentheses being multiplied?

#### MarkFL

Staff member
Suppose you have:

$$\displaystyle (a+b)(c+d)$$

You want to take each term in the first factor, and multiply it by each term in the second factor:

$$\displaystyle ac+ad+bc+bd$$

What I did was to begin with the first term in the first factor and multiply it by each of the terms in the second factor, and then do the same for the second term in the first factor.

You could also do it in two steps:

$$\displaystyle (a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd$$

When you are finished, you then want to combine like terms, if there are any. Can you use this method on the two examples you posted?