Verified answer

Answer:

5x - 1 and x + 5g

Step-by-step explanation:

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Answer:

5*(x+y)*(x-y)

Step-by-step explanation:

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

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

2) Pull out like factors :

 5x2 - 5y2  =   5 • (x2 - y2)

3) Factoring:  x2 - y2

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+) • (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 :  y2  is the square of  y1

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

FINAL RESULT:

 5 * (x + y) * (x - y)