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3x+11
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3x+11
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2\left(x^{2}+4x+4\right)-\left(2x-1\right)\left(x+3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
2x^{2}+8x+8-\left(2x-1\right)\left(x+3\right)
Use the distributive property to multiply 2 by x^{2}+4x+4.
2x^{2}+8x+8-\left(2x^{2}+5x-3\right)
Use the distributive property to multiply 2x-1 by x+3 and combine like terms.
2x^{2}+8x+8-2x^{2}-5x+3
To find the opposite of 2x^{2}+5x-3, find the opposite of each term.
8x+8-5x+3
Combine 2x^{2} and -2x^{2} to get 0.
3x+8+3
Combine 8x and -5x to get 3x.
3x+11
Add 8 and 3 to get 11.
2\left(x^{2}+4x+4\right)-\left(2x-1\right)\left(x+3\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
2x^{2}+8x+8-\left(2x-1\right)\left(x+3\right)
Use the distributive property to multiply 2 by x^{2}+4x+4.
2x^{2}+8x+8-\left(2x^{2}+5x-3\right)
Use the distributive property to multiply 2x-1 by x+3 and combine like terms.
2x^{2}+8x+8-2x^{2}-5x+3
To find the opposite of 2x^{2}+5x-3, find the opposite of each term.
8x+8-5x+3
Combine 2x^{2} and -2x^{2} to get 0.
3x+8+3
Combine 8x and -5x to get 3x.
3x+11
Add 8 and 3 to get 11.
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}