How do you factor #9(x^2+8x+16)+12(x+4)+4#?

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Answer 1 · 2015-05-15T22:00:00

Since you have the quadratic in this form, first note that

#x^2+8x+16 = (x+4)(x+4) = (x+4)^2#

So we are looking for factors of #9(x+4)^2+12(x+4)+4#

Note further that #9# and #4# are both square numbers, being #3^2# and #2^2#. Note also that #12# is twice #3*2#, so

#9(x+4)^2+12(x+4)+4 = (3(x+4)+2)^2#

#3(x+4)+2 = 3x+12+2 = 3x+14#

Putting this all together:

#9(x^2+8x+16)+12(x+4)+4 = (3x+14)^2#