How do you factor 9t ^ { 2} + 16t + 49t2+16t+4?

1 Answer
Aymeric D.
May 14, 2017

1/9(9t+8-2sqrt7)(9t+8+2sqrt7)19(9t+8−2√7)(9t+8+2√7)

Explanation:

9t^2+16t+4 = 3^2t^2 + 2*3*(8/3)t+(8/3)^2-(8/3)^2+4 9t2+16t+4=32t2+2⋅3⋅(83)t+(83)2−(83)2+4
= (3^2t^2 + 2*3*(8/3)t+(8/3)^2)-(8/3)^2+4 =(32t2+2⋅3⋅(83)t+(83)2)−(83)2+4
= (3t+8/3)^2-4(4/3)^2+4 =(3t+83)2−4(43)2+4
=(3t+8/3)^2+4(1-16/9)=(3t+83)2+4(1−169)
=(3t+8/3)^2+4((9-16)/9)=(3t+83)2+4(9−169)
=(3t+8/3)^2-4/9*7=(3t+83)2−49⋅7
=(3t+8/3)^2-((2sqrt7)/3)^2=(3t+83)2−(2√73)2
=(3t+8/3-(2sqrt7)/3)(3t+8/3+(2sqrt7)/3)=(3t+83−2√73)(3t+83+2√73)

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