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Factor squared:
y^4-y^2-8
-y^4+y^2-7
y^4-9*y^2+1
-y^2-4*y+3
Factor polynomial:
x^2-y^2+x-y
x^3+y^6
x^6+8
x^3*c^2-x^3*d^2
Least common denominator:
(sin(4*x)/((2+2*x)*8)+sin(2*x)/2+x/2)/2
(sin(2*x)/2+x)/2
(c*(v/k+1)+t)/((n+k)*(v/k+1)-k)
(a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))/(a-b)+(2*sqrt(b))/(sqrt(a)+sqrt(b))
How do you in partial fractions?:
z/(z+4)^2-z/z^2-16
-2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3))
(a+4)*a/2+(4*a+16)/(4*a^2+a^3)
((9*b)/(a-b))*((a^2-a*b)/(45*b))
Identical expressions
y^ four - nine *y^ two + one
y to the power of 4 minus 9 multiply by y squared plus 1
y to the power of four minus nine multiply by y to the power of two plus one
y4-9*y2+1
y⁴-9*y²+1
y to the power of 4-9*y to the power of 2+1
y^4-9y^2+1
y4-9y2+1
Similar expressions
y^4+9*y^2+1
y^4-9*y^2-1

Expression simplification/ Factor perfect squares/ y^4-9*y^2+1

Factor y^4-9*y^2+1 squared

The solution

You have entered [src]

 4      2    
y  - 9*y  + 1

$$\left(y^{4} - 9 y^{2}\right) + 1$$

y^4 - 9*y^2 + 1

Factorization [src]

/         ____________\ /         ____________\ /         ____________\ /         ____________\
|        /       ____ | |        /       ____ | |        /       ____ | |        /       ____ |
|       /  9   \/ 77  | |       /  9   \/ 77  | |       /  9   \/ 77  | |       /  9   \/ 77  |
|x +   /   - - ------ |*|x -   /   - - ------ |*|x +   /   - + ------ |*|x -   /   - + ------ |
\    \/    2     2    / \    \/    2     2    / \    \/    2     2    / \    \/    2     2    /

$$\left(x - \sqrt{\frac{9}{2} - \frac{\sqrt{77}}{2}}\right) \left(x + \sqrt{\frac{9}{2} - \frac{\sqrt{77}}{2}}\right) \left(x + \sqrt{\frac{\sqrt{77}}{2} + \frac{9}{2}}\right) \left(x - \sqrt{\frac{\sqrt{77}}{2} + \frac{9}{2}}\right)$$

(((x + sqrt(9/2 - sqrt(77)/2))*(x - sqrt(9/2 - sqrt(77)/2)))*(x + sqrt(9/2 + sqrt(77)/2)))*(x - sqrt(9/2 + sqrt(77)/2))

General simplification [src]

     4      2
1 + y  - 9*y

$$y^{4} - 9 y^{2} + 1$$

1 + y^4 - 9*y^2

The perfect square

Let's highlight the perfect square of the square three-member
$$\left(y^{4} - 9 y^{2}\right) + 1$$
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
$$a = 1$$
$$b = -9$$
$$c = 1$$
Then
$$m = - \frac{9}{2}$$
$$n = - \frac{77}{4}$$
So,
$$\left(y^{2} - \frac{9}{2}\right)^{2} - \frac{77}{4}$$

Assemble expression [src]

     4      2
1 + y  - 9*y

$$y^{4} - 9 y^{2} + 1$$

1 + y^4 - 9*y^2

Numerical answer [src]

1.0 + y^4 - 9.0*y^2

1.0 + y^4 - 9.0*y^2

Combining rational expressions [src]

     2 /      2\
1 + y *\-9 + y /

$$y^{2} \left(y^{2} - 9\right) + 1$$

1 + y^2*(-9 + y^2)

Common denominator [src]

     4      2
1 + y  - 9*y

$$y^{4} - 9 y^{2} + 1$$

1 + y^4 - 9*y^2

Rational denominator [src]

     4      2
1 + y  - 9*y

$$y^{4} - 9 y^{2} + 1$$

1 + y^4 - 9*y^2

Trigonometric part [src]

     4      2
1 + y  - 9*y

$$y^{4} - 9 y^{2} + 1$$

1 + y^4 - 9*y^2

Powers [src]

     4      2
1 + y  - 9*y

$$y^{4} - 9 y^{2} + 1$$

1 + y^4 - 9*y^2

Combinatorics [src]

     4      2
1 + y  - 9*y

$$y^{4} - 9 y^{2} + 1$$

1 + y^4 - 9*y^2

Other calculators

How to use it?

Identical expressions

Similar expressions

Factor y^4-9*y^2+1 squared

The solution