Question

factorize 27x^3+125y^3+135x^2y+225xy^2​

Answer 1

Answer:

Answer:

27x3+135x2y+225xy2+125y3

Final result :

(3x + 5y)3

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(((27•(x3))+((135•(x2))•y))+(225x•(y2)))+53y3

Step 2 :

Equation at the end of step 2 :

(((27•(x3))+((135•(x2))•y))+(32•52xy2))+53y3

Step 3 :

Equation at the end of step 3 :

(((27•(x3))+((33•5x2)•y))+(32•52xy2))+53y3

Step 4 :

Equation at the end of step 4 :

((33x3 + (33•5x2y)) + (32•52xy2)) + 53y3

Step 5 :

Checking for a perfect cube :

5.1 Factoring: 27x3+135x2y+225xy2+125y3

.

27x3+135x2y+225xy2+125y3 is a perfect cube which means it is the cube of another polynomial

In our case, the cubic root of 27x3+135x2y+225xy2+125y3 is 3x+5y

Factorization is (3x+5y)3

Final result :

(3x + 5y)3

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Answer 2

Answer:

Step by Step Solution

STEP  1  :

Equation at the end of step 1

 (((27•(x3))+((135•(x2))•y))+(225x•(y2)))+53y3

STEP 2 --  

Equation at the end of step 2 :

 (((27•(x3))+((135•(x2))•y))+(32•52xy2))+53y3

STEP  3  :

Equation at the end of step  3  :  

  (((27•(x3))+((33•5x2)•y))+(32•52xy2))+53y3

STEP 4   :

Equation at the end of step 4 :

 ((33x3 +  (33•5x2y)) +  (32•52xy2)) +  53y3

STEP 5

 Checking for a perfect cube

Factoring:  27x3+135x2y+225xy2+125y3  

 27x3+135x2y+225xy2+125y3  is a perfect cube which means it is the cube of another polynomial  

In our case, the cubic root of  27x3+135x2y+225xy2+125y3  is  3x+5y  

Factorization is  (3x+5y)3

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