The Total solution for NCERT class 6-12
x3 + 6x2 + 12x + 16= (x)3 + 3.x2.2 + 3.x.4 + (2)3 +8 {∵ a3 + 3a2b + 3ab2 +b3 =(a + b)3}= (x + 2)3 + 8 = (x + 2)3 + (2)3= (x + 2 + 2) [(x + 2)2 – (x + 2) x 2 + (2)2]{∵ a3 +b2 = (a + b) (a2 – ab + b2}= (x + 4) (x2 + 4x + 4 – 2x – 4 + 4)= (x + 4) (x2 + 2x + 4)