Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- 64*c^2*d^4-4*n^6
- a*m^2+b*m^2-c*n-b*n+c*m^2-a*n
- x^3+64
- x1*x2+x1^2*x3^2+x2*x3
- Least common denominator:
- -x/10-10*(x/10)^2/2
- cos(a)/2*sin(2)-1-sin(a)/2*cos(2)-1
- (z^5-5*z^3+10*z-1/10*z+1/5*z^3-1/z^5)*(z^3-3*z+1/3*z-1/z^3)
- ((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)
- Factor squared:
- y^4-y^2-7
- 5*p^4-3*p^2+13
- -5*b^2-2*b+1
- 2*p^4+p^2-2
- How do you in partial fractions?:
- ((p+3)/(p^2-2p))*((4p-8)/(p+3))
- (a^-2-a/a^-1-1)/(a^2+1)
- 6/(c-1)-10/(((c-1)^2)*10*(c^2))-1-2*c+2/c-1
- (t^4+9)/(t^4+9t^2)
-
Identical expressions
- - five *b^ two - two *b+ one
- minus 5 multiply by b squared minus 2 multiply by b plus 1
- minus five multiply by b to the power of two minus two multiply by b plus one
- -5*b2-2*b+1
- -5*b²-2*b+1
- -5*b to the power of 2-2*b+1
- -5b^2-2b+1
- -5b2-2b+1
-
Similar expressions
- 5*b^2-2*b+1
- -5*b^2+2*b+1
- -5*b^2-2*b-1
Factor -5*b^2-2*b+1 squared
The solution
Factorization
[src]
/ ___\ / ___\ | 1 \/ 6 | | 1 \/ 6 | |b + - - -----|*|b + - + -----| \ 5 5 / \ 5 5 /
$$\left(b + \left(\frac{1}{5} - \frac{\sqrt{6}}{5}\right)\right) \left(b + \left(\frac{1}{5} + \frac{\sqrt{6}}{5}\right)\right)$$
(b + 1/5 - sqrt(6)/5)*(b + 1/5 + sqrt(6)/5)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- 5 b^{2} - 2 b\right) + 1$$
To do this, let's use the formula
$$a b^{2} + b^{2} + c = a \left(b + m\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -5$$
$$b = -2$$
$$c = 1$$
Then
$$m = \frac{1}{5}$$
$$n = \frac{6}{5}$$
So,
$$\frac{6}{5} - 5 \left(b + \frac{1}{5}\right)^{2}$$
$$\left(- 5 b^{2} - 2 b\right) + 1$$
To do this, let's use the formula
$$a b^{2} + b^{2} + c = a \left(b + m\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -5$$
$$b = -2$$
$$c = 1$$
Then
$$m = \frac{1}{5}$$
$$n = \frac{6}{5}$$
So,
$$\frac{6}{5} - 5 \left(b + \frac{1}{5}\right)^{2}$$
Combining rational expressions
[src]
1 + b*(-2 - 5*b)
$$b \left(- 5 b - 2\right) + 1$$
1 + b*(-2 - 5*b)