SOLUTION: Good evening tutor, I do not understand multiplying polynomials. Could someone please help me with this problem? Multiply the following: (x/3 + 3/4)(3x/4 - 3/5) Th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Good evening tutor, I do not understand multiplying polynomials. Could someone please help me with this problem? Multiply the following: (x/3 + 3/4)(3x/4 - 3/5) Th      Log On


   

Question 94748This question is from textbook Beginning Algebra
: Good evening tutor,
I do not understand multiplying polynomials. Could someone please help me with this problem?
Multiply the following:
(x/3 + 3/4)(3x/4 - 3/5)
Thank you in advance for your help I am going crazy trying to understand this. This question is from textbook Beginning Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the following:
%28x%2F3+%2B+3%2F4%29 * %283x%2F4+-+3%2F5%29
:
We need to put each pair of fractions over a single denominator, using a common
denominator much as you do in numerical fractions:
:
Find the common denominator of the 1st pair: It would be 12, right?
%28x%2F3+%2B+3%2F4%29 = %284x+%2B+3%283%29%29%2F12 = %284x+%2B+9%29%2F12
:
Do the same with the 2nd pair of fractions, the common denominator would be 20:
%283x%2F4+-+3%2F5%29 = %284%283x%29+-+4%283%29%29%2F20%29 = %2815x+-+12%29%2F20%29
:
Now we have a single fraction times a single fraction
%284x+%2B+9%29%2F12 * %2815x+-+12%29%2F20%29
:
FOIL the numerators:
%2860x%5E2+-48x+%2B+135x+-+108%29%2F240 = %2860x%5E2+%2B+87x+-+108%29%2F240
:
Factor out 3 in the numerator, then cancel it into the denominator:
3%2820x%5E2+%2B+29x+-+36%29%2F240 = %2820x%5E2+%2B+29x+-+36%29%2F80; that's about all you can do with this
:
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