Mister Exam

Other calculators

Expression simplification/ Factor perfect squares/ -y^2-y*x-8*x^2

Factor -y^2-y*x-8*x^2 squared

An expression to simplify:

The solution

You have entered [src] 
   2            2
- y  - y*x - 8*x
$$- 8 x^{2} + \left(- x y - y^{2}\right)$$ 
-y^2 - y*x - 8*x^2
General simplification [src] 
   2      2      
- y  - 8*x  - x*y
$$- 8 x^{2} - x y - y^{2}$$ 
-y^2 - 8*x^2 - x*y
The perfect square
Let's highlight the perfect square of the square three-member
$$- 8 x^{2} + \left(- x y - y^{2}\right)$$
Let us write down the identical expression
$$- 8 x^{2} + \left(- x y - y^{2}\right) = - \frac{31 y^{2}}{32} + \left(- 8 x^{2} - x y - \frac{y^{2}}{32}\right)$$
or
$$- 8 x^{2} + \left(- x y - y^{2}\right) = - \frac{31 y^{2}}{32} - \left(2 \sqrt{2} x + \frac{\sqrt{2} y}{8}\right)^{2}$$
Factorization [src] 
/      /         ____\\ /      /        ____\\
|    y*\-1 + I*\/ 31 /| |    y*\1 + I*\/ 31 /|
|x - -----------------|*|x + ----------------|
\            16       / \           16       /
$$\left(x - \frac{y \left(-1 + \sqrt{31} i\right)}{16}\right) \left(x + \frac{y \left(1 + \sqrt{31} i\right)}{16}\right)$$ 
(x - y*(-1 + i*sqrt(31))/16)*(x + y*(1 + i*sqrt(31))/16)
Numerical answer [src] 
-y^2 - 8.0*x^2 - x*y
-y^2 - 8.0*x^2 - x*y
Assemble expression [src] 
   2      2      
- y  - 8*x  - x*y
$$- 8 x^{2} - x y - y^{2}$$ 
-y^2 - 8*x^2 - x*y
Combinatorics [src] 
   2      2      
- y  - 8*x  - x*y
$$- 8 x^{2} - x y - y^{2}$$ 
-y^2 - 8*x^2 - x*y
Common denominator [src] 
   2      2      
- y  - 8*x  - x*y
$$- 8 x^{2} - x y - y^{2}$$ 
-y^2 - 8*x^2 - x*y
Trigonometric part [src] 
   2      2      
- y  - 8*x  - x*y
$$- 8 x^{2} - x y - y^{2}$$ 
-y^2 - 8*x^2 - x*y
Combining rational expressions [src] 
     2             
- 8*x  + y*(-x - y)
$$- 8 x^{2} + y \left(- x - y\right)$$ 
-8*x^2 + y*(-x - y)
Rational denominator [src] 
   2      2      
- y  - 8*x  - x*y
$$- 8 x^{2} - x y - y^{2}$$ 
-y^2 - 8*x^2 - x*y
Powers [src] 
   2      2      
- y  - 8*x  - x*y
$$- 8 x^{2} - x y - y^{2}$$ 
-y^2 - 8*x^2 - x*y
    © Mister Exam – Calculator