SOLUTION: Write each expression in simplest form 4r2 - 25s2 / 2r2 + 3rs

SOLUTION: Write each expression in simplest form 4r2 - 25s2 / 2r2 + 3rs - 20s2 Thank you!!!

Question 44140: Write each expression in simplest form

4r2 - 25s2 / 2r2 + 3rs - 20s2
Thank you!!!
Answer by benni1013(206) (Show Source): You can put this solution on YOUR website!
4r2 - 25s2 / 2r2 + 3rs - 20s2
Let's look at the numerator first:
4r^2-25s^2==>(2r-5s)(2r+5s)
This is a special factoring case called the difference of squares. This occurs when you have two perfect square numbers in this case 4 and 25. Find the square root of both numbers. In this case 2 and 5 then set one quantity with a positive and one with a negative.
Now let's take a look at the denominator:
2r^2+3rs-20s^2==>2r^2+8rs-5rs-20s^2==>(2r^2+8rs)-(5rs-20s^2)==>2r(r+4s)-5s(r+4s)
The first step we need to take is to multiply the coefficients of the first and third terms of the trinomial in order to start the factoring. So the question ask yourself is what factors of -40 equals positive 3? The answer is 8 and -5. Now separate as shown above in the second step. Grouup together as shown in the third step. Fourth step is to start factoring by finding the GCF. At the fifth step you need to make sure that the quantities inside the parentheses are the same if they are not you messed up somewhere. In the end you will have the following:
(2r-5s)(r+4s)
Now in fraction form you will have:
(2r-5s)(2r+5s)/(2r-5s)(r+4s)
The only thing you have to do to finish the problem is cancel the 2r-5s from the numerator and the denominator leaving you with the answer (2r+5s)/(r+4s).
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