Simplify.

6x2x-8

9y2

6x3 - 89y2

Step by step solution:

Step 1:

Equation at the end of step 1:

((6 • (x2)) • x) - 89y2

Step 2:

Equation at the end of step 2:

((2•3x2) • x) - 89y2

Step 3:

Trying to factor as a Difference of Cubes:

3.1 Factoring: 6x3-89y2

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 : 6 is not a cube!

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

Final result:

6x3 - 89y2