Mister Exam
Factor polynomial y^3-2*y^2*z-4*y*z+8*z^2
The solution
You have entered
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3 2 2 y - 2*y *z - 4*y*z + 8*z
$$8 z^{2} + \left(- 4 y z + \left(y^{3} - 2 y^{2} z\right)\right)$$
y^3 - 2*y^2*z - 4*y*z + 8*z^2
General simplification
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3 2 2 y + 8*z - 4*y*z - 2*z*y
$$y^{3} - 2 y^{2} z - 4 y z + 8 z^{2}$$
y^3 + 8*z^2 - 4*y*z - 2*z*y^2
Factorization
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/ ___\ / ___\ \y + 2*\/ z /*\y - 2*\/ z /*(y - 2*z)
$$\left(y - 2 \sqrt{z}\right) \left(y + 2 \sqrt{z}\right) \left(y - 2 z\right)$$
((y + 2*sqrt(z))*(y - 2*sqrt(z)))*(y - 2*z)
Combining rational expressions
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2 8*z + y*(-4*z + y*(y - 2*z))
$$y \left(y \left(y - 2 z\right) - 4 z\right) + 8 z^{2}$$
8*z^2 + y*(-4*z + y*(y - 2*z))
Rational denominator
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3 2 2 y + 8*z - 4*y*z - 2*z*y
$$y^{3} - 2 y^{2} z - 4 y z + 8 z^{2}$$
y^3 + 8*z^2 - 4*y*z - 2*z*y^2
Assemble expression
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3 2 / 2\ y + 8*z + z*\-4*y - 2*y /
$$y^{3} + 8 z^{2} + z \left(- 2 y^{2} - 4 y\right)$$
3 2 2 y + 8*z - 4*y*z - 2*z*y
$$y^{3} - 2 y^{2} z - 4 y z + 8 z^{2}$$
y^3 + 8*z^2 - 4*y*z - 2*z*y^2
Powers
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3 2 2 y + 8*z - 4*y*z - 2*z*y
$$y^{3} - 2 y^{2} z - 4 y z + 8 z^{2}$$
y^3 + 8*z^2 - 4*y*z - 2*z*y^2
Trigonometric part
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3 2 2 y + 8*z - 4*y*z - 2*z*y
$$y^{3} - 2 y^{2} z - 4 y z + 8 z^{2}$$
y^3 + 8*z^2 - 4*y*z - 2*z*y^2
Combinatorics
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/ 2 \ (y - 2*z)*\y - 4*z/
$$\left(y - 2 z\right) \left(y^{2} - 4 z\right)$$
(y - 2*z)*(y^2 - 4*z)
Common denominator
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3 2 2 y + 8*z - 4*y*z - 2*z*y
$$y^{3} - 2 y^{2} z - 4 y z + 8 z^{2}$$
y^3 + 8*z^2 - 4*y*z - 2*z*y^2