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.