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Simplificación de expresiones/ Expresar el cuadrado perfecto/ -y^4-6*y^2-10

Descomponer -y^4-6*y^2-10 al cuadrado

Expresión a simplificar:

Solución

Ha introducido [src] 
   4      2     
- y  - 6*y  - 10
(−y4−6y2)−10\left(- y^{4} - 6 y^{2}\right) - 10 
-y^4 - 6*y^2 - 10
Expresión del cuadrado perfecto
Expresemos el cuadrado perfecto del trinomio cuadrático
(−y4−6y2)−10\left(- y^{4} - 6 y^{2}\right) - 10
Para eso usemos la fórmula
ay4+by2+c=a(m+y2)2+na y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n
donde
m=b2am = \frac{b}{2 a}
n=4ac−b24an = \frac{4 a c - b^{2}}{4 a}
En nuestro caso
a=−1a = -1
b=−6b = -6
c=−10c = -10
Entonces
m=3m = 3
n=−1n = -1
Pues,
−(y2+3)2−1- \left(y^{2} + 3\right)^{2} - 1
Simplificación general [src] 
       4      2
-10 - y  - 6*y
−y4−6y2−10- y^{4} - 6 y^{2} - 10 
-10 - y^4 - 6*y^2
Factorización [src] 
/    4 ____    /atan(1/3)\     4 ____    /atan(1/3)\\ /    4 ____    /atan(1/3)\     4 ____    /atan(1/3)\\ /      4 ____    /atan(1/3)\     4 ____    /atan(1/3)\\ /      4 ____    /atan(1/3)\     4 ____    /atan(1/3)\\
|x + \/ 10 *sin|---------| + I*\/ 10 *cos|---------||*|x + \/ 10 *sin|---------| - I*\/ 10 *cos|---------||*|x + - \/ 10 *sin|---------| + I*\/ 10 *cos|---------||*|x + - \/ 10 *sin|---------| - I*\/ 10 *cos|---------||
\              \    2    /               \    2    // \              \    2    /               \    2    // \                \    2    /               \    2    // \                \    2    /               \    2    //
(x+(104sin⁡(atan⁡(13)2)−104icos⁡(atan⁡(13)2)))(x+(104sin⁡(atan⁡(13)2)+104icos⁡(atan⁡(13)2)))(x+(−104sin⁡(atan⁡(13)2)+104icos⁡(atan⁡(13)2)))(x+(−104sin⁡(atan⁡(13)2)−104icos⁡(atan⁡(13)2)))\left(x + \left(\sqrt[4]{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)} - \sqrt[4]{10} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)}\right)\right) \left(x + \left(\sqrt[4]{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)} + \sqrt[4]{10} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)} + \sqrt[4]{10} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{10} \sin{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)} - \sqrt[4]{10} i \cos{\left(\frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{2} \right)}\right)\right) 
(((x + 10^(1/4)*sin(atan(1/3)/2) + i*10^(1/4)*cos(atan(1/3)/2))*(x + 10^(1/4)*sin(atan(1/3)/2) - i*10^(1/4)*cos(atan(1/3)/2)))*(x - 10^(1/4)*sin(atan(1/3)/2) + i*10^(1/4)*cos(atan(1/3)/2)))*(x - 10^(1/4)*sin(atan(1/3)/2) - i*10^(1/4)*cos(atan(1/3)/2))
Respuesta numérica [src] 
-10.0 - y^4 - 6.0*y^2
-10.0 - y^4 - 6.0*y^2
Combinatoria [src] 
       4      2
-10 - y  - 6*y
−y4−6y2−10- y^{4} - 6 y^{2} - 10 
-10 - y^4 - 6*y^2
Denominador común [src] 
       4      2
-10 - y  - 6*y
−y4−6y2−10- y^{4} - 6 y^{2} - 10 
-10 - y^4 - 6*y^2
Parte trigonométrica [src] 
       4      2
-10 - y  - 6*y
−y4−6y2−10- y^{4} - 6 y^{2} - 10 
-10 - y^4 - 6*y^2
Denominador racional [src] 
       4      2
-10 - y  - 6*y
−y4−6y2−10- y^{4} - 6 y^{2} - 10 
-10 - y^4 - 6*y^2
Unión de expresiones racionales [src] 
       2 /      2\
-10 + y *\-6 - y /
y2(−y2−6)−10y^{2} \left(- y^{2} - 6\right) - 10 
-10 + y^2*(-6 - y^2)
Compilar la expresión [src] 
       4      2
-10 - y  - 6*y
−y4−6y2−10- y^{4} - 6 y^{2} - 10 
-10 - y^4 - 6*y^2
Potencias [src] 
       4      2
-10 - y  - 6*y
−y4−6y2−10- y^{4} - 6 y^{2} - 10 
-10 - y^4 - 6*y^2
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