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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
1.gif (214 bytes)
= 4x + 2.gif (120 bytes)
= 4x + 2
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.)
(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.
Belleville lake was originally blue because it only had 11 algae plants. then towns and farms cropped up by the lake .this cause 446 more algae plants to grow which turned the lake
x/15=50/20
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