Mister Exam

Other calculators

Expression simplification/ Factor perfect squares/ -y^4-y^2+2

Factor -y^4-y^2+2 squared

An expression to simplify:

The solution

You have entered [src] 
   4    2    
- y  - y  + 2
$$\left(- y^{4} - y^{2}\right) + 2$$ 
-y^4 - y^2 + 2
General simplification [src] 
     2    4
2 - y  - y
$$- y^{4} - y^{2} + 2$$ 
2 - y^2 - y^4
Factorization [src] 
                /        ___\ /        ___\
(x + 1)*(x - 1)*\x + I*\/ 2 /*\x - I*\/ 2 /
$$\left(x - 1\right) \left(x + 1\right) \left(x + \sqrt{2} i\right) \left(x - \sqrt{2} i\right)$$ 
(((x + 1)*(x - 1))*(x + i*sqrt(2)))*(x - i*sqrt(2))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} - y^{2}\right) + 2$$
To do this, let's use the formula
$$a y^{4} + b y^{2} + c = a \left(m + y^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -1$$
$$b = -1$$
$$c = 2$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{9}{4}$$
So,
$$\frac{9}{4} - \left(y^{2} + \frac{1}{2}\right)^{2}$$
Numerical answer [src] 
2.0 - y^2 - y^4
2.0 - y^2 - y^4
Assemble expression [src] 
     2    4
2 - y  - y
$$- y^{4} - y^{2} + 2$$ 
2 - y^2 - y^4
Rational denominator [src] 
     2    4
2 - y  - y
$$- y^{4} - y^{2} + 2$$ 
2 - y^2 - y^4
Trigonometric part [src] 
     2    4
2 - y  - y
$$- y^{4} - y^{2} + 2$$ 
2 - y^2 - y^4
Combining rational expressions [src] 
     2 /      2\
2 + y *\-1 - y /
$$y^{2} \left(- y^{2} - 1\right) + 2$$ 
2 + y^2*(-1 - y^2)
Combinatorics [src] 
                  /     2\
-(1 + y)*(-1 + y)*\2 + y /
$$- \left(y - 1\right) \left(y + 1\right) \left(y^{2} + 2\right)$$ 
-(1 + y)*(-1 + y)*(2 + y^2)
Common denominator [src] 
     2    4
2 - y  - y
$$- y^{4} - y^{2} + 2$$ 
2 - y^2 - y^4
Powers [src] 
     2    4
2 - y  - y
$$- y^{4} - y^{2} + 2$$ 
2 - y^2 - y^4
    © Mister Exam – Calculator