Is the term factorable in this Algebra problem?

[Miike012]

Is this term factorable?

9a^2 - 6a + 1 -x^2 - 8dx - 16d^2

I don't see anything that I can group or any simple factors to factor out...

 

[PeterO]

Is this term factorable?

9a^2 - 6a + 1 -x^2 - 8dx - 16d^2

I don't see anything that I can group or any simple factors to factor out...

Group the first 3 and the second 3 with careful management of - signs

 

[Miike012]

9a^2 - 6a + 1 - (x^2 + 8dx + 16d^2)

= (3a - 1)^2 - (x + 4d)^2

= (3a - 1 + x + 4d)(3a - 1 - x - 4d)

How do you know what the roots are?

 

[PeterO]

9a^2 - 6a + 1 - (x^2 + 8dx + 16d^2)

= (3a - 1)^2 - (x + 4d)^2

= (3a - 1 + x + 4d)(3a - 1 - x - 4d)

How do you know what the roots are?

Not exactly sure what roots you are after? Expressions have factors - you have done that. Equations have roots - you don't have an equation?

EDIT: The following post spilled the beans about what I was trying to get you to think about.

 

[Bohrok]

If it were a function in x where a and d are unknown constants, you could set the factored expression equal to 0, solve for x, and express the roots in terms of a and d.

 

[Miike012]

thank you for your guys help.