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1+12x-9x^{2}
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1+12x-9x^{2}
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x^{2}-6x+9-2\left(5x-4\right)\left(-1+x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
x^{2}-6x+9+\left(-10x+8\right)\left(-1+x\right)
Use the distributive property to multiply -2 by 5x-4.
x^{2}-6x+9+18x-10x^{2}-8
Use the distributive property to multiply -10x+8 by -1+x and combine like terms.
x^{2}+12x+9-10x^{2}-8
Combine -6x and 18x to get 12x.
-9x^{2}+12x+9-8
Combine x^{2} and -10x^{2} to get -9x^{2}.
-9x^{2}+12x+1
Subtract 8 from 9 to get 1.
x^{2}-6x+9-2\left(5x-4\right)\left(-1+x\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
x^{2}-6x+9+\left(-10x+8\right)\left(-1+x\right)
Use the distributive property to multiply -2 by 5x-4.
x^{2}-6x+9+18x-10x^{2}-8
Use the distributive property to multiply -10x+8 by -1+x and combine like terms.
x^{2}+12x+9-10x^{2}-8
Combine -6x and 18x to get 12x.
-9x^{2}+12x+9-8
Combine x^{2} and -10x^{2} to get -9x^{2}.
-9x^{2}+12x+1
Subtract 8 from 9 to get 1.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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
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