(5rs-(1•(t3)))•(0-((3r2•s)•t)) Step 2 :Trying to factor as a Difference of Cubes: 2.1 Factoring: 5rs-t3
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 : 5 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Final result : (5rs - t3) • -3r2st