Question

factorise the following expression:-
$8^{3} +36p^{2} q+54pq^{2} +27q^{3}$

Answer 1

Answer:

(2p + 3q)3

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 (((8•(p3))+((36•(p2))•q))+(54p•(q2)))+33q3

Step  2  :

Equation at the end of step  2  :

 (((8•(p3))+((36•(p2))•q))+(2•33pq2))+33q3

Step  3  :

Equation at the end of step  3  :

 (((8•(p3))+((22•32p2)•q))+(2•33pq2))+33q3

Step  4  :

Equation at the end of step  4  :

 ((23p3 +  (22•32p2q)) +  (2•33pq2)) +  33q3

Step  5  :

Checking for a perfect cube :

Factoring:  8p3+36p2q+54pq2+27q3  

.

 8p3+36p2q+54pq2+27q3  is a perfect cube which means it is the cube of another polynomial  

In our case, the cubic root of  8p3+36p2q+54pq2+27q3  is  2p+3q  

Factorization is  (2p+3q)3

Final result :

 (2p + 3q)3