Question

How do you factor `9t ^ { 2} + 16t + 4`?

Answer 1

`1/9(9t+8-2sqrt7)(9t+8+2sqrt7)`

Explanation:

`9t^2+16t+4 = 3^2t^2 + 2*3*(8/3)t+(8/3)^2-(8/3)^2+4`
`= (3^2t^2 + 2*3*(8/3)t+(8/3)^2)-(8/3)^2+4`
`= (3t+8/3)^2-4(4/3)^2+4`
`=(3t+8/3)^2+4(1-16/9)`
`=(3t+8/3)^2+4((9-16)/9)`
`=(3t+8/3)^2-4/9*7`
`=(3t+8/3)^2-((2sqrt7)/3)^2`
`=(3t+8/3-(2sqrt7)/3)(3t+8/3+(2sqrt7)/3)`