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2+14x-14+\frac{1}{2}\left(x-1\right)\left(x-2\right)\times 24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Use the distributive property to multiply x-1 by 14.
-12+14x+\frac{1}{2}\left(x-1\right)\left(x-2\right)\times 24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Subtract 14 from 2 to get -12.
-12+14x+\frac{24}{2}\left(x-1\right)\left(x-2\right)+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Multiply \frac{1}{2} and 24 to get \frac{24}{2}.
-12+14x+12\left(x-1\right)\left(x-2\right)+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Divide 24 by 2 to get 12.
-12+14x+\left(12x-12\right)\left(x-2\right)+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Use the distributive property to multiply 12 by x-1.
-12+14x+12x^{2}-24x-12x+24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Apply the distributive property by multiplying each term of 12x-12 by each term of x-2.
-12+14x+12x^{2}-36x+24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Combine -24x and -12x to get -36x.
-12-22x+12x^{2}+24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Combine 14x and -36x to get -22x.
12-22x+12x^{2}+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Add -12 and 24 to get 12.
12-22x+12x^{2}+\frac{12}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)
Multiply \frac{1}{6} and 12 to get \frac{12}{6}.
12-22x+12x^{2}+2\left(x-1\right)\left(x-2\right)\left(x-3\right)
Divide 12 by 6 to get 2.
12-22x+12x^{2}+\left(2x-2\right)\left(x-2\right)\left(x-3\right)
Use the distributive property to multiply 2 by x-1.
12-22x+12x^{2}+\left(2x^{2}-4x-2x+4\right)\left(x-3\right)
Apply the distributive property by multiplying each term of 2x-2 by each term of x-2.
12-22x+12x^{2}+\left(2x^{2}-6x+4\right)\left(x-3\right)
Combine -4x and -2x to get -6x.
12-22x+12x^{2}+2x^{3}-6x^{2}-6x^{2}+18x+4x-12
Apply the distributive property by multiplying each term of 2x^{2}-6x+4 by each term of x-3.
12-22x+12x^{2}+2x^{3}-12x^{2}+18x+4x-12
Combine -6x^{2} and -6x^{2} to get -12x^{2}.
12-22x+12x^{2}+2x^{3}-12x^{2}+22x-12
Combine 18x and 4x to get 22x.
12-22x+2x^{3}+22x-12
Combine 12x^{2} and -12x^{2} to get 0.
12+2x^{3}-12
Combine -22x and 22x to get 0.
2x^{3}
Subtract 12 from 12 to get 0.
2+14x-14+\frac{1}{2}\left(x-1\right)\left(x-2\right)\times 24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Use the distributive property to multiply x-1 by 14.
-12+14x+\frac{1}{2}\left(x-1\right)\left(x-2\right)\times 24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Subtract 14 from 2 to get -12.
-12+14x+\frac{24}{2}\left(x-1\right)\left(x-2\right)+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Multiply \frac{1}{2} and 24 to get \frac{24}{2}.
-12+14x+12\left(x-1\right)\left(x-2\right)+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Divide 24 by 2 to get 12.
-12+14x+\left(12x-12\right)\left(x-2\right)+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Use the distributive property to multiply 12 by x-1.
-12+14x+12x^{2}-24x-12x+24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Apply the distributive property by multiplying each term of 12x-12 by each term of x-2.
-12+14x+12x^{2}-36x+24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Combine -24x and -12x to get -36x.
-12-22x+12x^{2}+24+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Combine 14x and -36x to get -22x.
12-22x+12x^{2}+\frac{1}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)\times 12
Add -12 and 24 to get 12.
12-22x+12x^{2}+\frac{12}{6}\left(x-1\right)\left(x-2\right)\left(x-3\right)
Multiply \frac{1}{6} and 12 to get \frac{12}{6}.
12-22x+12x^{2}+2\left(x-1\right)\left(x-2\right)\left(x-3\right)
Divide 12 by 6 to get 2.
12-22x+12x^{2}+\left(2x-2\right)\left(x-2\right)\left(x-3\right)
Use the distributive property to multiply 2 by x-1.
12-22x+12x^{2}+\left(2x^{2}-4x-2x+4\right)\left(x-3\right)
Apply the distributive property by multiplying each term of 2x-2 by each term of x-2.
12-22x+12x^{2}+\left(2x^{2}-6x+4\right)\left(x-3\right)
Combine -4x and -2x to get -6x.
12-22x+12x^{2}+2x^{3}-6x^{2}-6x^{2}+18x+4x-12
Apply the distributive property by multiplying each term of 2x^{2}-6x+4 by each term of x-3.
12-22x+12x^{2}+2x^{3}-12x^{2}+18x+4x-12
Combine -6x^{2} and -6x^{2} to get -12x^{2}.
12-22x+12x^{2}+2x^{3}-12x^{2}+22x-12
Combine 18x and 4x to get 22x.
12-22x+2x^{3}+22x-12
Combine 12x^{2} and -12x^{2} to get 0.
12+2x^{3}-12
Combine -22x and 22x to get 0.
2x^{3}
Subtract 12 from 12 to get 0.
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}