Simplify (4x^3y^-6) (2xy^6)

22xy6 • (2x3y - 3)

Reformatting the input:

Changes made to your input should not affect the solution:

(1) : "y6" was replaced by "y^6". 1 more similar replacement (s).

Step by step solution:

Step 1:

Equation at the end of step 1:

(((4 • (x3)) • y) - 6) • 2xy6

Step 2:

Equation at the end of step 2:

((22x3 • y) - 6) • 2xy6

Step 3:

Step 4:

Pulling out like terms:

4.1 Pull out like factors:

4x3y - 6 = 2 • (2x3y - 3)

Trying to factor as a Difference of Cubes:

4.2 Factoring: 2x3y - 3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 + ab + b2)

Proof : (a-b) • (a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3 + (a2b-ba2) + (ab2-b2a) - b3 =

a3+0+0+b3 =

a3+b3

Check : 2 is not a cube!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Multiplying exponents:

4.3 21 multiplied by 21 = 2 (1 + 1) = 22

Final result:

22xy6 • (2x3y - 3)