Question

9x²+ 9y²-82xy =0
find xy​

Answer 1

Answer:

 9 • (x - y)2

Step-by-step explanation:

((9 • (x2)) -  18xy) +  32y2

STEP  

2

:

Equation at the end of step

2

:

 (32x2 -  18xy) +  32y2

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  9x2 - 18xy + 9y2  =   9 • (x2 - 2xy + y2)  

Trying to factor a multi variable polynomial :

4.2    Factoring    x2 - 2xy + y2  

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

Found a factorization  :  (x - y)•(x - y)

Detecting a perfect square :

4.3    x2  -2xy  +y2  is a perfect square  

It factors into  (x-y)•(x-y)

which is another way of writing  (x-y)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

Final result :

 9 • (x - y)2