SOLUTION: Find the missing term so that each expression is the square of a binomial. a) {{{x^2-________+9y^2}}} b) {{{64x^2+80x+________}}} Can you help me with this? Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the missing term so that each expression is the square of a binomial. a) {{{x^2-________+9y^2}}} b) {{{64x^2+80x+________}}} Can you help me with this? Thank you      Log On


   

Question 285294: Find the missing term so that each expression is the square of a binomial.
a) x%5E2-________%2B9y%5E2
b) 64x%5E2%2B80x%2B________
Can you help me with this?
Thank you
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Find the missing term so that each expression is the square of a binomial.
a) x%5E2-%22___%22%2B9y%5E2

That is the same as

%28x%29%5E2-%22___%22%2B%283y%29%5E2

and to be the square of a binomial, it would have to factor 
as

%28x-3y%29%28x-3y%29 

since that is the same as %28x-3y%29%5E2

FOILing that out:

%28x-3y%29%28x-3y%29

x%5E2-3xy-3xy%2B9y%5E2

x%5E2-6xy%2B9y%5E2

Comparing that to

x%5E2-%22___%22%2B9y%5E2

we see that 6xy is what goes in the blank.

b) 64x%5E2%2B80x%2B___

It has to factor like this, where N is some number:

%288x%2BN%29%288x%2BN%29

since that is the same as %288x%2BN%29%5E2

FOILing that out:

%288x%2BN%29%288x%2BN%29

64x%5E2%2B8Nx%2B8Nx%2BN%5E2

64x%5E2%2B16Nx%2BN%5E2

Comparing that to

64x%5E2%2B80x%2B___

we know that the middle terms must be equal,
so we set them equal to each other:

16Nx=80x
16N=80
N=5

Substituting in

64x%5E2%2B16Nx%2BN%5E2

64x%5E2%2B16%285%29x%2B%285%29%5E2

64x%5E2%2B80x%2B25

Comparing that again to

64x%5E2%2B80x%2B___

we see that 25 is what goes in the blank.

Edwin