Question

4st(s-t)-6s^2 (t-t^2)-3t^2(2 s^2-s)+2st (s-t)

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Answer 1

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "s2" was replaced by "s^2". 3 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((4st•(s-t))-((6•(s2))•(t-(t2))))-((3•(t2))•(((2•(s2))-s)+tea•(s-t)))
Step 2 :

Equation at the end of step 2 :

((4st•(s-t))-((6•(s2))•(t-(t2))))-((3•(t2))•((2s2-s)+tea•(s-t)))
Step 3 :

Equation at the end of step 3 :

((4st•(s-t))-((6•(s2))•(t-(t2))))-(3t2•(2s2+stea-s-t2ea))
Step 4 :

Equation at the end of step 4 :

((4st•(s-t))-((6•(s2))•(t-(t2))))-3t2•(2s2+stea-s-t2ea)
Step 5 :

Equation at the end of step 5 :

((4st•(s-t))-((2•3s2)•(t-t2)))-3t2•(2s2+stea-s-t2ea)
Step 6 :

Step 7 :

Pulling out like terms :

7.1 Pull out like factors :

t - t2 = -t • (t - 1)

Equation at the end of step 7 :

((4st•(s-t))-( -2•3s2t)•(t-1))-3t2•(2s2+stea-s-t2ea)
Step 8 :

Equation at the end of step 8 :

(4st•(s-t)-( -2•3s2t)•(t-1))-3t2•(2s2+stea-s-t2ea)
Step 9 :

Step 10 :

Pulling out like terms :

10.1 Pull out like factors :

-2s2t - 3st3ea - st2 + 3t4ea =

-t • (2s2 + 3st2ea + st - 3t3ea)

Checking for a perfect cube :

10.2 2s2 + 3st2ea + st - 3t3ea is not a perfect cube

Final result :

-t • (2s2 + 3st2ea + st - 3t3ea)

I hope it helps
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