SOLUTION: Multiplying Rational Expressions: Please provide a complete solution. 1. 10x-4x^2/4x^20x+25 * (2x^3-5x^2)

Question 795729: Multiplying Rational Expressions: Please provide a complete solution.
1. 10x-4x^2/4x^20x+25 * (2x^3-5x^2)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There seems to be some typos, but I am good at guessing.
If I did not guess right, ask again.
Calculating something like

is like calculating ,
but just like when working with fractions, it pays to cancel out common factors first.
So you need to factor all three polynomials.
(Long after the last test on factoring polynomials ends, the need to factor polynomials keeps coming back).

At this point, you have to realize that
So the last rational expression above can be written as
,
and now

NOTES:
1) When typing/writing in one line, you need to write

.
to mean .
Without parentheses,

means .
In algebra, as in any human language, f you use the wrong wording, you may be misunderstood. I can often guess what people mean, but calculators and computers do exactly what you ask, and getting what you asked for can get you in long lasting trouble. Working as a chemist, I saw people get in trouble because of missed parentheses when typing a calculation into the calculator.

2) Factoring polynomials is essential to survive all math way beyond the last test on factoring. If you think you can forget it, you are wrong. (I once made that mistake). And if you cannot master factoring polynomials now, you have to relearn it. (It does not seem overly useful in real life after school, but school math is a hurdle you have to overcome).
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