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-2x-10
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-2x-10
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-8x-\left(x^{2}-6x+9\right)+\left(x+1\right)\left(x-1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
-8x-x^{2}+6x-9+\left(x+1\right)\left(x-1\right)
To find the opposite of x^{2}-6x+9, find the opposite of each term.
-2x-x^{2}-9+\left(x+1\right)\left(x-1\right)
Combine -8x and 6x to get -2x.
-2x-x^{2}-9+x^{2}-1
Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
-2x-9-1
Combine -x^{2} and x^{2} to get 0.
-2x-10
Subtract 1 from -9 to get -10.
-8x-\left(x^{2}-6x+9\right)+\left(x+1\right)\left(x-1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
-8x-x^{2}+6x-9+\left(x+1\right)\left(x-1\right)
To find the opposite of x^{2}-6x+9, find the opposite of each term.
-2x-x^{2}-9+\left(x+1\right)\left(x-1\right)
Combine -8x and 6x to get -2x.
-2x-x^{2}-9+x^{2}-1
Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
-2x-9-1
Combine -x^{2} and x^{2} to get 0.
-2x-10
Subtract 1 from -9 to get -10.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
Arithmetic
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}