SOLUTION: Please help. I can not figure out how to do these. Thank you in advance! Multiply. 1. n squared +5n+4 OVER 2n squared+2n MULTIPLIED BY n squared-n-12 OVER n squared-16.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help. I can not figure out how to do these. Thank you in advance! Multiply. 1. n squared +5n+4 OVER 2n squared+2n MULTIPLIED BY n squared-n-12 OVER n squared-16.       Log On


   

Question 117491: Please help. I can not figure out how to do these. Thank you in advance!
Multiply.
1.
n squared +5n+4 OVER 2n squared+2n MULTIPLIED BY n squared-n-12 OVER n squared-16.

2.
3pq to the 3rd power OVER 5 DIVIDED BY 9p squared q squared OVER 10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28n%5E2%2B5n%2B4%29%2F%282n%5E2%2B2n%29%29%28%28n%5E2-n-12%29%2F%28n%5E2-16%29%29 Start with the given expression

Factor n%5E2%2B5n%2B4 to get %28n%2B4%29%28n%2B1%29

Factor 2n%5E2%2B2n to get 2n%28n%2B1%29

Factor n%5E2-n-12 to get %28n-4%29%28n%2B3%29

Factor n%5E2-16 to get %28n%2B4%29%28n-4%29


%28n%2B4%29%28n%2B1%29%28n-4%29%28n%2B3%29%2F2n%28n%2B1%29%28n%2B4%29%28n-4%29 Combine the fractions



Cancel like terms



%28n%2B3%29%2F%282n%29 Simplify


So %28%28n%5E2%2B5n%2B4%29%2F%282n%5E2%2B2n%29%29%28%28n%5E2-n-12%29%2F%28n%5E2-16%29%29 simplifies to %28n%2B3%29%2F%282n%29


In other words,





%283pq%5E3%2F5%29%2F%289p%5E2q%5E2%2F10%29 Start with the given expression



%2830pq%5E3%2F45p%5E2q%5E2%29 Combine the fractions by multiplying

p%5E%281-2%29q%5E%283-2%29 Remember when you divide monomials, you subtract their corresponding exponents. For instance x%5E2%2Fx%5E3=x%5E%282-3%29=x%5E-1


%282%2F3%29p%5E-1q%5E1 Simplify. Remember to reduce the coefficients (which are numbers in front of the variables) to get 30%2F45=2%2F3.


%282%2F3%29%281%2Fp%29q Rewrite p%5E-1 as 1%2Fp


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Answer:

So %283pq%5E3%2F5%29%2F%289p%5E2q%5E2%2F10%29 simplifies to %282%2F3%29%281%2Fp%29q.

In other words, %283pq%5E3%2F5%29%2F%289p%5E2q%5E2%2F10%29=%282%2F3%29%281%2Fp%29q.