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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.
Variation of Parameters Notice there the differential equation, y′′ + q (t) y′ + r (t) y = g (t) Suppose that y 1 (t) and y 2 (t) are a fundamental set of solutions for
* 2^(1/2)*4^(1/8)*8^(1/16)*16^(1/32) =
2 over 11 + 2 over 33
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
1+2+3+.....+n=1/2n(n+1)
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