SOLUTION: factor the polynomial completely using the grouping method * 9b^2 - 24b + 16 - a^2 * what I've tried: 3b (3b - 8) + (16-a^2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor the polynomial completely using the grouping method * 9b^2 - 24b + 16 - a^2 * what I've tried: 3b (3b - 8) + (16-a^2)      Log On


   

Question 707942: factor the polynomial completely using the grouping method
* 9b^2 - 24b + 16 - a^2
* what I've tried: 3b (3b - 8) + (16-a^2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9b^2 - 24b + 16 - a^2

(9b^2 - 24b + 16) - a^2

(9b^2 - 12b - 12b + 16) - a^2

((9b^2 - 12b) + (-12b + 16)) - a^2

(3b(3b - 4) - 4(3b - 4)) - a^2

(3b - 4)(3b - 4) - a^2

(3b - 4)^2 - a^2

(3b - 4 - a)(3b - 4 + a)

So 9b^2 - 24b + 16 - a^2 completely factors to (3b - 4 - a)(3b - 4 + a)