Question

How is the binomial 2x^2y-4xy^3 expresses in factores form

Answer 1

2xy • (x - 2y2)

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.