Sr Examen
Factorizar el polinomio y^2+x*y-x^3+2*x^2-x*y^2+2*y^2
Solución
Ha introducido
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2 3 2 2 2 y + x*y - x + 2*x - x*y + 2*y
$$2 y^{2} + \left(- x y^{2} + \left(2 x^{2} + \left(- x^{3} + \left(x y + y^{2}\right)\right)\right)\right)$$
y^2 + x*y - x^3 + 2*x^2 - x*y^2 + 2*y^2
Simplificación general
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3 2 2 2 - x + 2*x + 3*y + x*y - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + x y + 3 y^{2}$$
-x^3 + 2*x^2 + 3*y^2 + x*y - x*y^2
Factorización
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$$\left(x + \left(\frac{- 3 y^{2} + 3 y + 4}{3 \sqrt[3]{- \frac{63 y^{2}}{2} - 9 y + \frac{\sqrt{\left(- 63 y^{2} - 18 y - 16\right)^{2} - 4 \left(- 3 y^{2} + 3 y + 4\right)^{3}}}{2} - 8}} + \frac{\sqrt[3]{- \frac{63 y^{2}}{2} - 9 y + \frac{\sqrt{\left(- 63 y^{2} - 18 y - 16\right)^{2} - 4 \left(- 3 y^{2} + 3 y + 4\right)^{3}}}{2} - 8}}{3} - \frac{2}{3}\right)\right) \left(x + \left(\frac{- 3 y^{2} + 3 y + 4}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{63 y^{2}}{2} - 9 y + \frac{\sqrt{\left(- 63 y^{2} - 18 y - 16\right)^{2} - 4 \left(- 3 y^{2} + 3 y + 4\right)^{3}}}{2} - 8}} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{63 y^{2}}{2} - 9 y + \frac{\sqrt{\left(- 63 y^{2} - 18 y - 16\right)^{2} - 4 \left(- 3 y^{2} + 3 y + 4\right)^{3}}}{2} - 8}}{3} - \frac{2}{3}\right)\right) \left(x + \left(\frac{- 3 y^{2} + 3 y + 4}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{63 y^{2}}{2} - 9 y + \frac{\sqrt{\left(- 63 y^{2} - 18 y - 16\right)^{2} - 4 \left(- 3 y^{2} + 3 y + 4\right)^{3}}}{2} - 8}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{63 y^{2}}{2} - 9 y + \frac{\sqrt{\left(- 63 y^{2} - 18 y - 16\right)^{2} - 4 \left(- 3 y^{2} + 3 y + 4\right)^{3}}}{2} - 8}}{3} - \frac{2}{3}\right)\right)$$
((x - 2/3 + (-8 + sqrt((-16 - 63*y^2 - 18*y)^2 - 4*(4 - 3*y^2 + 3*y)^3)/2 - 9*y - 63*y^2/2)^(1/3)/3 + (4 - 3*y^2 + 3*y)/(3*(-8 + sqrt((-16 - 63*y^2 - 18*y)^2 - 4*(4 - 3*y^2 + 3*y)^3)/2 - 9*y - 63*y^2/2)^(1/3)))*(x - 2/3 + (-8 + sqrt((-16 - 63*y^2 - 18*y)^2 - 4*(4 - 3*y^2 + 3*y)^3)/2 - 9*y - 63*y^2/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 + (4 - 3*y^2 + 3*y)/(3*(-1/2 - i*sqrt(3)/2)*(-8 + sqrt((-16 - 63*y^2 - 18*y)^2 - 4*(4 - 3*y^2 + 3*y)^3)/2 - 9*y - 63*y^2/2)^(1/3))))*(x - 2/3 + (-8 + sqrt((-16 - 63*y^2 - 18*y)^2 - 4*(4 - 3*y^2 + 3*y)^3)/2 - 9*y - 63*y^2/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 + (4 - 3*y^2 + 3*y)/(3*(-1/2 + i*sqrt(3)/2)*(-8 + sqrt((-16 - 63*y^2 - 18*y)^2 - 4*(4 - 3*y^2 + 3*y)^3)/2 - 9*y - 63*y^2/2)^(1/3)))
Respuesta numérica
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-x^3 + 2.0*x^2 + 3.0*y^2 + x*y - x*y^2
-x^3 + 2.0*x^2 + 3.0*y^2 + x*y - x*y^2
Unión de expresiones racionales
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3 2 2 2 - x + 2*x + 2*y + y*(x + y) - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + 2 y^{2} + y \left(x + y\right)$$
-x^3 + 2*x^2 + 2*y^2 + y*(x + y) - x*y^2
Denominador común
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3 2 2 2 - x + 2*x + 3*y + x*y - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + x y + 3 y^{2}$$
-x^3 + 2*x^2 + 3*y^2 + x*y - x*y^2
Combinatoria
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3 2 2 2 - x + 2*x + 3*y + x*y - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + x y + 3 y^{2}$$
-x^3 + 2*x^2 + 3*y^2 + x*y - x*y^2
Parte trigonométrica
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3 2 2 2 - x + 2*x + 3*y + x*y - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + x y + 3 y^{2}$$
-x^3 + 2*x^2 + 3*y^2 + x*y - x*y^2
Denominador racional
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3 2 2 2 - x + 2*x + 3*y + x*y - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + x y + 3 y^{2}$$
-x^3 + 2*x^2 + 3*y^2 + x*y - x*y^2
Potencias
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3 2 2 2 - x + 2*x + 3*y + x*y - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + x y + 3 y^{2}$$
-x^3 + 2*x^2 + 3*y^2 + x*y - x*y^2
Compilar la expresión
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3 2 2 - x + 2*x + x*y + y *(3 - x)
$$- x^{3} + 2 x^{2} + x y + y^{2} \left(3 - x\right)$$
3 2 2 / 2\ - x + 2*x + 3*y + x*\y - y /
$$- x^{3} + 2 x^{2} + x \left(- y^{2} + y\right) + 3 y^{2}$$
3 2 2 2 - x + 2*x + 3*y + x*y - x*y
$$- x^{3} + 2 x^{2} - x y^{2} + x y + 3 y^{2}$$
-x^3 + 2*x^2 + 3*y^2 + x*y - x*y^2