Mister Exam

Other calculators

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

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

An expression to simplify:

The solution

You have entered [src] 
   4      2    
- y  + 4*y  + 2
$$\left(- y^{4} + 4 y^{2}\right) + 2$$ 
-y^4 + 4*y^2 + 2
General simplification [src] 
     4      2
2 - y  + 4*y
$$- y^{4} + 4 y^{2} + 2$$ 
2 - y^4 + 4*y^2
Factorization [src] 
/         ____________\ /         ____________\ /       ___________\ /       ___________\
|        /        ___ | |        /        ___ | |      /       ___ | |      /       ___ |
\x + I*\/  -2 + \/ 6  /*\x - I*\/  -2 + \/ 6  /*\x + \/  2 + \/ 6  /*\x - \/  2 + \/ 6  /
$$\left(x - i \sqrt{-2 + \sqrt{6}}\right) \left(x + i \sqrt{-2 + \sqrt{6}}\right) \left(x + \sqrt{2 + \sqrt{6}}\right) \left(x - \sqrt{2 + \sqrt{6}}\right)$$ 
(((x + i*sqrt(-2 + sqrt(6)))*(x - i*sqrt(-2 + sqrt(6))))*(x + sqrt(2 + sqrt(6))))*(x - sqrt(2 + sqrt(6)))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- y^{4} + 4 y^{2}\right) + 2$$
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
$$a = -1$$
$$b = 4$$
$$c = 2$$
Then
$$m = -2$$
$$n = 6$$
So,
$$6 - \left(y^{2} - 2\right)^{2}$$
Combining rational expressions [src] 
     2 /     2\
2 + y *\4 - y /
$$y^{2} \left(4 - y^{2}\right) + 2$$ 
2 + y^2*(4 - y^2)
Rational denominator [src] 
     4      2
2 - y  + 4*y
$$- y^{4} + 4 y^{2} + 2$$ 
2 - y^4 + 4*y^2
Trigonometric part [src] 
     4      2
2 - y  + 4*y
$$- y^{4} + 4 y^{2} + 2$$ 
2 - y^4 + 4*y^2
Common denominator [src] 
     4      2
2 - y  + 4*y
$$- y^{4} + 4 y^{2} + 2$$ 
2 - y^4 + 4*y^2
Numerical answer [src] 
2.0 - y^4 + 4.0*y^2
2.0 - y^4 + 4.0*y^2
Powers [src] 
     4      2
2 - y  + 4*y
$$- y^{4} + 4 y^{2} + 2$$ 
2 - y^4 + 4*y^2
Assemble expression [src] 
     4      2
2 - y  + 4*y
$$- y^{4} + 4 y^{2} + 2$$ 
2 - y^4 + 4*y^2
Combinatorics [src] 
     4      2
2 - y  + 4*y
$$- y^{4} + 4 y^{2} + 2$$ 
2 - y^4 + 4*y^2
    © Mister Exam – Calculator