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\frac{1}{4}x^{2}+3x+9-\left(\frac{1}{2}x-3\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}x+3\right)^{2}.
\frac{1}{4}x^{2}+3x+9-\left(\frac{1}{4}x^{2}-3x+9\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{1}{2}x-3\right)^{2}.
\frac{1}{4}x^{2}+3x+9-\frac{1}{4}x^{2}+3x-9
To find the opposite of \frac{1}{4}x^{2}-3x+9, find the opposite of each term.
3x+9+3x-9
Combine \frac{1}{4}x^{2} and -\frac{1}{4}x^{2} to get 0.
6x+9-9
Combine 3x and 3x to get 6x.
6x
Subtract 9 from 9 to get 0.
\frac{1}{4}x^{2}+3x+9-\left(\frac{1}{2}x-3\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}x+3\right)^{2}.
\frac{1}{4}x^{2}+3x+9-\left(\frac{1}{4}x^{2}-3x+9\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{1}{2}x-3\right)^{2}.
\frac{1}{4}x^{2}+3x+9-\frac{1}{4}x^{2}+3x-9
To find the opposite of \frac{1}{4}x^{2}-3x+9, find the opposite of each term.
3x+9+3x-9
Combine \frac{1}{4}x^{2} and -\frac{1}{4}x^{2} to get 0.
6x+9-9
Combine 3x and 3x to get 6x.
6x
Subtract 9 from 9 to get 0.
Examples
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{ 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}