Mister Exam
Factor polynomial a*m^2+b*m^2-c*n-b*n+c*m^2-a*n
The solution
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2 2 2 a*m + b*m - c*n - b*n + c*m - a*n
$$- a n + \left(c m^{2} + \left(- b n + \left(- c n + \left(a m^{2} + b m^{2}\right)\right)\right)\right)$$
a*m^2 + b*m^2 - c*n - b*n + c*m^2 - a*n
General simplification
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2 2 2 a*m + b*m + c*m - a*n - b*n - c*n
$$a m^{2} - a n + b m^{2} - b n + c m^{2} - c n$$
a*m^2 + b*m^2 + c*m^2 - a*n - b*n - c*n
Numerical answer
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a*m^2 + b*m^2 + c*m^2 - a*n - b*n - c*n
a*m^2 + b*m^2 + c*m^2 - a*n - b*n - c*n
Combinatorics
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/ 2 \ \m - n/*(a + b + c)
$$\left(m^{2} - n\right) \left(a + b + c\right)$$
(m^2 - n)*(a + b + c)
Powers
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2 2 2 a*m + b*m + c*m - a*n - b*n - c*n
$$a m^{2} - a n + b m^{2} - b n + c m^{2} - c n$$
a*m^2 + b*m^2 + c*m^2 - a*n - b*n - c*n
Trigonometric part
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2 2 2 a*m + b*m + c*m - a*n - b*n - c*n
$$a m^{2} - a n + b m^{2} - b n + c m^{2} - c n$$
a*m^2 + b*m^2 + c*m^2 - a*n - b*n - c*n
Combining rational expressions
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2 2 c*m + m *(a + b) - a*n - b*n - c*n
$$- a n - b n + c m^{2} - c n + m^{2} \left(a + b\right)$$
c*m^2 + m^2*(a + b) - a*n - b*n - c*n
Rational denominator
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2 2 2 a*m + b*m + c*m - a*n - b*n - c*n
$$a m^{2} - a n + b m^{2} - b n + c m^{2} - c n$$
a*m^2 + b*m^2 + c*m^2 - a*n - b*n - c*n
Assemble expression
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/ 2 \ 2 b*\m - n/ + n*(-a - c) + m *(a + c)
$$b \left(m^{2} - n\right) + m^{2} \left(a + c\right) + n \left(- a - c\right)$$
2 / 2 \ / 2 \ a*m + b*\m - n/ + c*\m - n/ - a*n
$$a m^{2} - a n + b \left(m^{2} - n\right) + c \left(m^{2} - n\right)$$
2 2 2 a*m + b*m + c*m - a*n - b*n - c*n
$$a m^{2} - a n + b m^{2} - b n + c m^{2} - c n$$
2 2 / 2 \ a*m + b*m + c*\m - n/ + n*(-a - b)
$$a m^{2} + b m^{2} + c \left(m^{2} - n\right) + n \left(- a - b\right)$$
/ 2 \ 2 b*\m - n/ + m *(a + c) - a*n - c*n
$$- a n + b \left(m^{2} - n\right) - c n + m^{2} \left(a + c\right)$$
2 n*(-a - b - c) + m *(a + b + c)
$$m^{2} \left(a + b + c\right) + n \left(- a - b - c\right)$$
/ 2 \ 2 a*\m - n/ + m *(b + c) - b*n - c*n
$$a \left(m^{2} - n\right) - b n - c n + m^{2} \left(b + c\right)$$
2 2 2 a*m + b*m + c*m + n*(-a - b - c)
$$a m^{2} + b m^{2} + c m^{2} + n \left(- a - b - c\right)$$
/ 2 \ / 2 \ / 2 \ a*\m - n/ + b*\m - n/ + c*\m - n/
$$a \left(m^{2} - n\right) + b \left(m^{2} - n\right) + c \left(m^{2} - n\right)$$
/ 2 \ 2 c*\m - n/ + m *(a + b) - a*n - b*n
$$- a n - b n + c \left(m^{2} - n\right) + m^{2} \left(a + b\right)$$
2 2 a*m + n*(-a - b - c) + m *(b + c)
$$a m^{2} + m^{2} \left(b + c\right) + n \left(- a - b - c\right)$$
/ 2 \ 2 c*\m - n/ + n*(-a - b) + m *(a + b)
$$c \left(m^{2} - n\right) + m^{2} \left(a + b\right) + n \left(- a - b\right)$$
/ 2 \ 2 / 2 \ a*\m - n/ + b*m + c*\m - n/ - b*n
$$a \left(m^{2} - n\right) + b m^{2} - b n + c \left(m^{2} - n\right)$$
2 m *(a + b + c) - a*n - b*n - c*n
$$- a n - b n - c n + m^{2} \left(a + b + c\right)$$
2 2 / 2 \ a*m + b*m + c*\m - n/ - a*n - b*n
$$a m^{2} - a n + b m^{2} - b n + c \left(m^{2} - n\right)$$
2 / 2 \ 2 a*m + b*\m - n/ + c*m - a*n - c*n
$$a m^{2} - a n + b \left(m^{2} - n\right) + c m^{2} - c n$$
2 / 2 \ 2 a*m + b*\m - n/ + c*m + n*(-a - c)
$$a m^{2} + b \left(m^{2} - n\right) + c m^{2} + n \left(- a - c\right)$$
/ 2 \ 2 2 a*\m - n/ + b*m + c*m - b*n - c*n
$$a \left(m^{2} - n\right) + b m^{2} - b n + c m^{2} - c n$$
/ 2 \ / 2 \ 2 a*\m - n/ + b*\m - n/ + c*m - c*n
$$a \left(m^{2} - n\right) + b \left(m^{2} - n\right) + c m^{2} - c n$$
a*(m^2 - n) + b*(m^2 - n) + c*m^2 - c*n
Common denominator
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2 2 2 a*m + b*m + c*m - a*n - b*n - c*n
$$a m^{2} - a n + b m^{2} - b n + c m^{2} - c n$$
a*m^2 + b*m^2 + c*m^2 - a*n - b*n - c*n