Explain How to Distribute simplifying expressions?

The distributive law states that for all numbers a, b, and c,

a(b + c)= ab + ac

What does this mean in plain language? It means if you want to multiply a by a sum of two (or more) terms, like b + c, you can just multiply by each term seperately.

For example, if you want to multiply 3 by x + 2, you just multply 3 by each of the terms x and 2:

3(x + 2)

= 3 - x + 3 - 2 (You don't usually bother to write this step)

= 3x + 6

Some more examples

Example.

x(x + 2y)

= x + 2 xy

Example.

1.gif (214 bytes)

= 4x + 2.gif (120 bytes)

= 4x + 2

Example.

3x + 4(y + 10)

= 3x + 4y + 40

(Why didn't the 3x get distributed? Because its not part of the multiplication. The only thing being multiplied by y + 10 is 4.)

Example.

(3x + 4)(y + 10)

= (3x + 4) y + (3x + 4) 10

Cool, huh? I distributed the entire expression 3x + 4. Parentheses are required! By the way, we can still distribute some more if we want.

= 3xy + 4y + 30x + 40.