Answer:

STEP

1

:

Equation at the end of step 1

(2x • (y3)) - (2x3 • y)

STEP

2

:

Equation at the end of step

2

:

2xy3 - 2x3y

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

2xy3 - 2x3y = -2xy • (x2 - y2)

Trying to factor as a Difference of Squares:

4.2 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 :

-2xy • (x + y) • (x - y)