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5x^{2}-10x+3
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5x^{2}-10x+3
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\left(x-1\right)\left(4x-2-1\right)+x\left(x-3\right)
Combine x and 3x to get 4x.
\left(x-1\right)\left(4x-3\right)+x\left(x-3\right)
Subtract 1 from -2 to get -3.
4x^{2}-3x-4x+3+x\left(x-3\right)
Apply the distributive property by multiplying each term of x-1 by each term of 4x-3.
4x^{2}-7x+3+x\left(x-3\right)
Combine -3x and -4x to get -7x.
4x^{2}-7x+3+x^{2}-3x
Use the distributive property to multiply x by x-3.
5x^{2}-7x+3-3x
Combine 4x^{2} and x^{2} to get 5x^{2}.
5x^{2}-10x+3
Combine -7x and -3x to get -10x.
\left(x-1\right)\left(4x-2-1\right)+x\left(x-3\right)
Combine x and 3x to get 4x.
\left(x-1\right)\left(4x-3\right)+x\left(x-3\right)
Subtract 1 from -2 to get -3.
4x^{2}-3x-4x+3+x\left(x-3\right)
Apply the distributive property by multiplying each term of x-1 by each term of 4x-3.
4x^{2}-7x+3+x\left(x-3\right)
Combine -3x and -4x to get -7x.
4x^{2}-7x+3+x^{2}-3x
Use the distributive property to multiply x by x-3.
5x^{2}-7x+3-3x
Combine 4x^{2} and x^{2} to get 5x^{2}.
5x^{2}-10x+3
Combine -7x and -3x to get -10x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}