Simplify (5rs-1t3) (-3r2st).

(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