SOLUTION: factor the polynomial by grouping 81a^2-27ab-18b^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor the polynomial by grouping 81a^2-27ab-18b^2      Log On


   



Question 191267: factor the polynomial by grouping
81a^2-27ab-18b^2

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

81a%5E2-27ab-18b%5E2

First factor out 9

9%289a%5E2-3ab-2b%5E2%29

In the parentheses, multiply the first coefficient 9
by the last coefficient 2, getting 18.  Write down
all pairs of integer factors whose product is 18.
They are

1*18
2*9
3*6

Since the last sign in the parentheses is -, we
subtract those, larger minus smaller:

18-1 = 17
9-2 = 7
6-3 = 3


Since the middle coefficient of %289a%5E2-3ab-2b%5E2%29
is 3, and since 3 = 6-3 we write -3ab as -6ab+3ab

9%289a%5E2-6ab%2B3ab-2b%5E2%29

Factor the first two terms in the parentheses by factoring 
out 3a

9%283a%283a-2b%29%2B3ab-2b%5E2%29
 
Factor the last two terms in the parentheses by factoring 
out b

9%283a%283a-2b%29%2Bb%283a-2b%29%29

Inside the parentheses take out %283a-2b%29

9%283a-2b%29%283a%2Bb%29

Edwin