Mister Exam
Factor x*x^2/2-18*(x^2-6*x+9) squared
The solution
You have entered
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2 x*x / 2 \ ---- - 18*\x - 6*x + 9/ 2
$$\frac{x x^{2}}{2} - 18 \left(\left(x^{2} - 6 x\right) + 9\right)$$
(x*x^2)/2 - 18*(x^2 - 6*x + 9)
General simplification
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3
x 2
-162 + -- - 18*x + 108*x
2
$$\frac{x^{3}}{2} - 18 x^{2} + 108 x - 162$$
-162 + x^3/2 - 18*x^2 + 108*x
Factorization
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/ ________________ / ___\ \ / ________________ / ___\ \ / ________________ \ | 3 / ___ | 1 I*\/ 3 | 24 | | 3 / ___ | 1 I*\/ 3 | 24 | | 3 / ___ 24 | |x + -12 - 3*\/ 22 + 2*I*\/ 7 *|- - - -------| - -----------------------------------|*|x + -12 - 3*\/ 22 + 2*I*\/ 7 *|- - + -------| - -----------------------------------|*|x + -12 - 3*\/ 22 + 2*I*\/ 7 - -------------------| | \ 2 2 / ________________ / ___\| | \ 2 2 / ________________ / ___\| | ________________| | 3 / ___ | 1 I*\/ 3 || | 3 / ___ | 1 I*\/ 3 || | 3 / ___ | | \/ 22 + 2*I*\/ 7 *|- - - -------|| | \/ 22 + 2*I*\/ 7 *|- - + -------|| \ \/ 22 + 2*I*\/ 7 / \ \ 2 2 // \ \ 2 2 //
$$\left(x + \left(-12 - \frac{24}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{22 + 2 \sqrt{7} i}} - 3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{22 + 2 \sqrt{7} i}\right)\right) \left(x + \left(-12 - 3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{22 + 2 \sqrt{7} i} - \frac{24}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{22 + 2 \sqrt{7} i}}\right)\right) \left(x + \left(-12 - 3 \sqrt[3]{22 + 2 \sqrt{7} i} - \frac{24}{\sqrt[3]{22 + 2 \sqrt{7} i}}\right)\right)$$
((x - 12 - 3*(22 + 2*i*sqrt(7))^(1/3)*(-1/2 - i*sqrt(3)/2) - 24/((22 + 2*i*sqrt(7))^(1/3)*(-1/2 - i*sqrt(3)/2)))*(x - 12 - 3*(22 + 2*i*sqrt(7))^(1/3)*(-1/2 + i*sqrt(3)/2) - 24/((22 + 2*i*sqrt(7))^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x - 12 - 3*(22 + 2*i*sqrt(7))^(1/3) - 24/(22 + 2*i*sqrt(7))^(1/3))
Fraction decomposition
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-162 + x^3/2 - 18*x^2 + 108*x
$$\frac{x^{3}}{2} - 18 x^{2} + 108 x - 162$$
3
x 2
-162 + -- - 18*x + 108*x
2
Rational denominator
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3 2
-324 + x - 36*x + 216*x
-------------------------
2
$$\frac{x^{3} - 36 x^{2} + 216 x - 324}{2}$$
(-324 + x^3 - 36*x^2 + 216*x)/2
Assemble expression
[src]
3
x 2
-162 + -- - 18*x + 108*x
2
$$\frac{x^{3}}{2} - 18 x^{2} + 108 x - 162$$
-162 + x^3/2 - 18*x^2 + 108*x
Powers
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3
x 2
-162 + -- - 18*x + 108*x
2
$$\frac{x^{3}}{2} - 18 x^{2} + 108 x - 162$$
-162 + x^3/2 - 18*x^2 + 108*x
Trigonometric part
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3
x 2
-162 + -- - 18*x + 108*x
2
$$\frac{x^{3}}{2} - 18 x^{2} + 108 x - 162$$
-162 + x^3/2 - 18*x^2 + 108*x
Combinatorics
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3
x 2
-162 + -- - 18*x + 108*x
2
$$\frac{x^{3}}{2} - 18 x^{2} + 108 x - 162$$
-162 + x^3/2 - 18*x^2 + 108*x
Combining rational expressions
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3
-324 + x - 36*x*(-6 + x)
-------------------------
2
$$\frac{x^{3} - 36 x \left(x - 6\right) - 324}{2}$$
(-324 + x^3 - 36*x*(-6 + x))/2
Common denominator
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3
x 2
-162 + -- - 18*x + 108*x
2
$$\frac{x^{3}}{2} - 18 x^{2} + 108 x - 162$$
-162 + x^3/2 - 18*x^2 + 108*x