Mister Exam

Other calculators

Expression simplification/ Factorization polynomials/ -y^3-5*x^2*y+x^4+5*x^4-7*x^2*y+6*y^3

Factor polynomial -y^3-5*x^2*y+x^4+5*x^4-7*x^2*y+6*y^3

An expression to simplify:

The solution

You have entered [src] 
   3      2      4      4      2        3
- y  - 5*x *y + x  + 5*x  - 7*x *y + 6*y
$$6 y^{3} + \left(- 7 x^{2} y + \left(5 x^{4} + \left(x^{4} + \left(- 5 x^{2} y - y^{3}\right)\right)\right)\right)$$ 
-y^3 - 5*x^2*y + x^4 + 5*x^4 - 7*x^2*y + 6*y^3
General simplification [src] 
   3      4         2
5*y  + 6*x  - 12*y*x
$$6 x^{4} - 12 x^{2} y + 5 y^{3}$$ 
5*y^3 + 6*x^4 - 12*y*x^2
Factorization [src] 
/         _________________________\ /         _________________________\ /         _________________________\ /         _________________________\
|        /         ___   _________ | |        /         ___   _________ | |        /         ___   _________ | |        /         ___   _________ |
|       /      y*\/ 6 *\/ 6 - 5*y  | |       /      y*\/ 6 *\/ 6 - 5*y  | |       /      y*\/ 6 *\/ 6 - 5*y  | |       /      y*\/ 6 *\/ 6 - 5*y  |
|x +   /   y - ------------------- |*|x -   /   y - ------------------- |*|x +   /   y + ------------------- |*|x -   /   y + ------------------- |
\    \/                 6          / \    \/                 6          / \    \/                 6          / \    \/                 6          /
$$\left(x - \sqrt{- \frac{\sqrt{6} y \sqrt{6 - 5 y}}{6} + y}\right) \left(x + \sqrt{- \frac{\sqrt{6} y \sqrt{6 - 5 y}}{6} + y}\right) \left(x + \sqrt{\frac{\sqrt{6} y \sqrt{6 - 5 y}}{6} + y}\right) \left(x - \sqrt{\frac{\sqrt{6} y \sqrt{6 - 5 y}}{6} + y}\right)$$ 
(((x + sqrt(y - y*sqrt(6)*sqrt(6 - 5*y)/6))*(x - sqrt(y - y*sqrt(6)*sqrt(6 - 5*y)/6)))*(x + sqrt(y + y*sqrt(6)*sqrt(6 - 5*y)/6)))*(x - sqrt(y + y*sqrt(6)*sqrt(6 - 5*y)/6))
Common denominator [src] 
   3      4         2
5*y  + 6*x  - 12*y*x
$$6 x^{4} - 12 x^{2} y + 5 y^{3}$$ 
5*y^3 + 6*x^4 - 12*y*x^2
Numerical answer [src] 
6.0*x^4 + 5.0*y^3 - 12.0*y*x^2
6.0*x^4 + 5.0*y^3 - 12.0*y*x^2
Combinatorics [src] 
   3      4         2
5*y  + 6*x  - 12*y*x
$$6 x^{4} - 12 x^{2} y + 5 y^{3}$$ 
5*y^3 + 6*x^4 - 12*y*x^2
Trigonometric part [src] 
   3      4         2
5*y  + 6*x  - 12*y*x
$$6 x^{4} - 12 x^{2} y + 5 y^{3}$$ 
5*y^3 + 6*x^4 - 12*y*x^2
Rational denominator [src] 
   3      4         2
5*y  + 6*x  - 12*y*x
$$6 x^{4} - 12 x^{2} y + 5 y^{3}$$ 
5*y^3 + 6*x^4 - 12*y*x^2
Powers [src] 
   3      4         2
5*y  + 6*x  - 12*y*x
$$6 x^{4} - 12 x^{2} y + 5 y^{3}$$ 
5*y^3 + 6*x^4 - 12*y*x^2
Assemble expression [src] 
   3      4         2
5*y  + 6*x  - 12*y*x
$$6 x^{4} - 12 x^{2} y + 5 y^{3}$$ 
5*y^3 + 6*x^4 - 12*y*x^2
Combining rational expressions [src] 
   4      3     /   2      2\        2
6*x  + 6*y  + y*\- y  - 5*x / - 7*y*x
$$6 x^{4} - 7 x^{2} y + 6 y^{3} + y \left(- 5 x^{2} - y^{2}\right)$$ 
6*x^4 + 6*y^3 + y*(-y^2 - 5*x^2) - 7*y*x^2
    © Mister Exam – Calculator