Which expression is equivalent to 9x^2-2y+3x^2-3y

The answer is choice B

Step-by-step explanation: (3x-2y)2-(2x-3y)2  

Final result :

 5 • (x + y) • (x - y)

Step by step solution :

Step  1  :

1.1     Evaluate :  (3x-2y)2   =    9x2-12xy+4y2  

1.2     Evaluate :  (2x-3y)2   =    4x2-12xy+9y2  

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  5x2 - 5y2  =   5 • (x2 - y2)  

Trying to factor as a Difference of Squares :

2.2      Factoring:  x2 - y2  

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 :  x2  is the square of  x1  

Check :  y2  is the square of  y1  

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

Final result :

 5 • (x + y) • (x - y)

c. (3,2,6) is the answer.