81 x

3y + 72x
2y
2 + 16xy
3

Step 1 :Equation at the end of step 1

 ((81•(x4))-((72•(x2))•(y2)))+24y4

Step 2 :

Equation at the end of step 2 :

 ((81 • (x4)) -  ((23•32x2) • y2)) +  24y4

Step 3 :

Equation at the end of step 3 :

 (34x4 -  (23•32x2y2)) +  24y4

Step 4 :Trying to factor a multi variable polynomial

4.1    Factoring    81x4 - 72x2y2 + 16y4

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

Found a factorization  :  (9x2 - 4y2)•(9x2 - 4y2)

Detecting a perfect square :

4.2    81x4  -72x2y2  +16y4  is a perfect square

It factors into  (9x2-4y2)•(9x2-4y2)

which is another way of writing  (9x2-4y2)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

Trying to factor as a Difference of Squares:

4.3      Factoring:  9x2-4y2

Put the exponent aside, try to factor  9x2-4y2

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  9  is the square of  3

Check : 4 is the square of 2

Check :  x2  is the square of  x1

Check :  y2  is the square of  y1

Factorization is :       (3x + 2y)  •  (3x - 2y)

Raise to the exponent which was put aside

Factorization becomes :   (3x + 2y)2   •  (3x - 2y)2  

Final result :

 (3x + 2y)2 • (3x - 2y)2

Step-by-step explanation:

81x+16y

should be the correct one

the correct answer to your question is a. 4^4

good luck my friend!

hope this !

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! < 3

have a splendid day < 3 : )