Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4+9*y^2-6
- y^4-y^2-1
- y^4+9*y^2+2
- x^4-x^2+1
- Factor polynomial:
- x^5+x+1
- x^2-x+1
- x^2-4*x-5
- x^2-x-1
- Least common denominator:
- z/t-t/z
- z-8/z^2/3*z^(1/3)+4
- y/(y+3)^2-y/(y^2)-9
- ((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5
- How do you in partial fractions?:
- (((z^2)+(6*z+4))/((z^3)+8))/(1/-1)
- ((z^2+1)^2/(4*z^2))/(13+12*((z^2+1)/2*z*z))
- (x^2-25)/(x^2+3*x-40)
- y/(y+3)^2-y/(y^2)-9
- Derivative of:
-
x^4-2*x^2+1
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Identical expressions
- x^ four - two *x^ two + one
- x to the power of 4 minus 2 multiply by x squared plus 1
- x to the power of four minus two multiply by x to the power of two plus one
- x4-2*x2+1
- x⁴-2*x²+1
- x to the power of 4-2*x to the power of 2+1
- x^4-2x^2+1
- x4-2x2+1
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Similar expressions
- x^4-2*x^2-1
- x^4+2*x^2+1
Factor x^4-2*x^2+1 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{4} - 2 x^{2}\right) + 1$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -2$$
$$c = 1$$
Then
$$m = -1$$
$$n = 0$$
So,
$$\left(x^{2} - 1\right)^{2}$$
$$\left(x^{4} - 2 x^{2}\right) + 1$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -2$$
$$c = 1$$
Then
$$m = -1$$
$$n = 0$$
So,
$$\left(x^{2} - 1\right)^{2}$$
Combinatorics
[src]
2 2 (1 + x) *(-1 + x)
$$\left(x - 1\right)^{2} \left(x + 1\right)^{2}$$
(1 + x)^2*(-1 + x)^2
Combining rational expressions
[src]
2 / 2\ 1 + x *\-2 + x /
$$x^{2} \left(x^{2} - 2\right) + 1$$
1 + x^2*(-2 + x^2)