Question

How do you factor this expression: x^3 + 9x^2 + 27x + 27

Answer 1

Step  1  :

Equation at the end of step  1  :

 (((x3) +  32x2) +  27x) +  27

Step  2  :

Checking for a perfect cube :

2.1    Factoring:  x3+9x2+27x+27  

.

 x3+9x2+27x+27  is a perfect cube which means it is the cube of another polynomial  

In our case, the cubic root of  x3+9x2+27x+27  is  x+3  

Factorization is  (x+3)3

Final result :

 (x + 3)3

Answer 2

Answer:

$\large\boxed{x^3+9x^2+27x+27=(x+3)^3=(x+3)(x+3)(x+3)}$

Step-by-step explanation:

$\text{Use}\ (a+b)^3=a^3+3a^3b+3ab^2+b^3\\\\x^3+9x^2+27x+27=x^3+3(x^2)(3)+3(x)(3^2)+3^3=(x+3)^3$