Answer:
2xy • (x - 2y2)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((2 • (x2)) • y) - 22xy3
STEP 2
Equation at the end of step
(2x2 • y) - 22xy3
STEP
3
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2x2y - 4xy3 = 2xy • (x - 2y2)
Trying to factor as a Difference of Squares:
4.2 Factoring: x - 2y2
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 : 2 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
