Mister Exam
Factor polynomial 8*c^2*d^2+36*c^2*d^3+6*c*d^6
The solution
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2 2 2 3 6 8*c *d + 36*c *d + 6*c*d
$$6 c d^{6} + \left(8 c^{2} d^{2} + 36 c^{2} d^{3}\right)$$
(8*c^2)*d^2 + (36*c^2)*d^3 + (6*c)*d^6
Factorization
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/ 4 \ | 3*d | c*|c + --------|*d \ 4 + 18*d/
$$d c \left(c + \frac{3 d^{4}}{18 d + 4}\right)$$
(c*(c + 3*d^4/(4 + 18*d)))*d
General simplification
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2 / 4 \ 2*c*d *\3*d + 4*c + 18*c*d/
$$2 c d^{2} \left(18 c d + 4 c + 3 d^{4}\right)$$
2*c*d^2*(3*d^4 + 4*c + 18*c*d)
Numerical answer
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8.0*c^2*d^2 + 6.0*c*d^6 + 36.0*c^2*d^3
8.0*c^2*d^2 + 6.0*c*d^6 + 36.0*c^2*d^3
Rational denominator
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6 2 2 2 3 6*c*d + 8*c *d + 36*c *d
$$36 c^{2} d^{3} + 8 c^{2} d^{2} + 6 c d^{6}$$
6*c*d^6 + 8*c^2*d^2 + 36*c^2*d^3
Combinatorics
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2 / 4 \ 2*c*d *\3*d + 4*c + 18*c*d/
$$2 c d^{2} \left(18 c d + 4 c + 3 d^{4}\right)$$
2*c*d^2*(3*d^4 + 4*c + 18*c*d)
Trigonometric part
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6 2 2 2 3 6*c*d + 8*c *d + 36*c *d
$$36 c^{2} d^{3} + 8 c^{2} d^{2} + 6 c d^{6}$$
6*c*d^6 + 8*c^2*d^2 + 36*c^2*d^3
Common denominator
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6 2 2 2 3 6*c*d + 8*c *d + 36*c *d
$$36 c^{2} d^{3} + 8 c^{2} d^{2} + 6 c d^{6}$$
6*c*d^6 + 8*c^2*d^2 + 36*c^2*d^3
Assemble expression
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6 2 2 2 3 6*c*d + 8*c *d + 36*c *d
$$36 c^{2} d^{3} + 8 c^{2} d^{2} + 6 c d^{6}$$
2 / 2 3\ 6 c *\8*d + 36*d / + 6*c*d
$$c^{2} \left(36 d^{3} + 8 d^{2}\right) + 6 c d^{6}$$
c^2*(8*d^2 + 36*d^3) + 6*c*d^6
Combining rational expressions
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2 / 4 \ 2*c*d *\3*d + 2*c*(2 + 9*d)/
$$2 c d^{2} \left(2 c \left(9 d + 2\right) + 3 d^{4}\right)$$
2*c*d^2*(3*d^4 + 2*c*(2 + 9*d))
Powers
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6 2 2 2 3 6*c*d + 8*c *d + 36*c *d
$$36 c^{2} d^{3} + 8 c^{2} d^{2} + 6 c d^{6}$$
6*c*d^6 + 8*c^2*d^2 + 36*c^2*d^3