Question

How do you factor : 48x^2+72x+27?

I know the GCF which is 3 but I am not sure how to use the perfect square patterns on this problem after I have found the GCF?

Answer 1

`3(4x+3)^2`

Explanation:

`16x^2+24x+9`

`4^2` is `16` and `3^2` is `9`

`(4x+3)(4x+3)`

`4x*4x = 16x^2`

`4x*3 + 4x*3 = 12x + 12x = 24x`

`3*3 = 9`

`16x^2+24x+9 = (4x+3)^2`

`48x^2+72x+27 = 3(4x+3)^2`

Answer 2

`3(4x + 3)^2`

Explanation:

Use the new AC method to factor trinomials (Socratic Search)
`y = 48x^2 + 72x + 27 =` 48(x + p)(x + q)
Converted trinomial:
`ý = x^2 + 72 x + 1296 = (x + 36)^2`.
We have (p')= (q') = (36).
Therefor, `p = q = (p')/a = 36/48 = 3/4`
Factored form:
`y = 48(x + 3/4)^2 = 3(4x + 3)^2`