Answer:

 (x + 4y)3

 —————————

     9    

Step-by-step explanation:

STEP

1

:

           x + 4y

Simplify   ——————

             3    

Equation at the END of step

1

:

 ((((x2)+8XY)+(16•(y2)))1)  (x+4y)

 —————————————————————————•——————

             3               3    

STEP  

2

:

Equation at the end of step

2

:

 ((((x2)+8xy)+(24y2))1)  (x+4y)

 ——————————————————————•——————

           3              3    

STEP

3

:

           x2 + 8xy + 16y2

Simplify   ———————————————

                  3        

Trying to factor a multi variable polynomial :

3.1    Factoring    x2 + 8xy + 16y2  

Try to factor this multi-variable trinomial using trial and error  

Found a factorization  :  (x + 4y)•(x + 4y)

DETECTING a perfect square :

3.2    x2  +8xy  +16y2  is a perfect square  

It factors into  (x+4y)•(x+4y)

which is another way of writing  (x+4y)2

How to recognize a perfect square trinomial:  

• It has three terms  

• Two of its terms are perfect squares themselves  

• The remaining term is twice the product of the square ROOTS of the other two terms

Equation at the end of step

3

:

 (x + 4y)2   (x + 4y)

 ————————— • ————————

     3          3    

STEP

4

:

Multiplying EXPONENTIAL Expressions:

4.1    Multiply  (x+4y)2   by  (x+4y)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x+4y)  and the exponents are :

         2

and   1 , as  (x+4y)  is the same number as  (x+4y)1  

The product is therefore,  (x+4y)(2+1) = (x+4y)3  

Final result :

 (x + 4y)3

 —————————

     9