How do you factor 9(x+4)^2+12(x+4)+49(x+4)2+12(x+4)+4?

1 Answer
Alan P.
Mar 31, 2018

9(x+4)^2+12(x+4)+4 =color(blue)((3x+14)^2)9(x+4)2+12(x+4)+4=(3x+14)2

Explanation:

You could expand each of the terms and then collect like terms before attempting to factor, but it is probably easier to temporarily substitute a variable for (x+4)(x+4); for example with k=x+4k=x+4 we would have:

9k^2+12k+49k2+12k+4

which factors fairly easily into (3k+2)^2(3k+2)2

then replacing the kk with x+4x+4
we get (3(x+4)+2)^2=(3x+14)^2(3(x+4)+2)2=(3x+14)2

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