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?

2 Answers
Brandon
Mar 1, 2018

#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#

Nghi N
Mar 1, 2018

#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#

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