College algebra - factoring problem?

[rory_meaursault]

The problem is 49a^2 - 126a + 81.

I hate using the guess and check method, but the Big X/Butterfly/Square/whatever involves multiplying coefficients A and C and leaving B alone to get you started leaves a big number that makes my life miserable.

Any ideas on how to solve this smoothly?

 

[BigGlenntheHeavy]

\(\displaystyle 49a^2-126a+81 \ = \ (7a)^2-126a+(9)^2.\)

\(\displaystyle Now, \ does \ (2)(7)(9) \ = \ 126? \ Yes, \ it \ does, \ ergo \ we \ have:\)

\(\displaystyle (7a-9)(7a-9) \ = \ (7a-9)^2, \ a \ perfect \ square.\)

 

[rory_meaursault]

You have no idea how silly I feel right now.

Me and my making things overly complex without needing to.

Thanks so much!

 

[mmm4444bot]

the Big X/Butterfly/Square/whatever involves multiplying

I simply have no ideas about what schools teach anymore.