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5x^{2}+13x+3
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5x^{2}+13x+3
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5\left(x^{2}+2x+1\right)+3\left(x+1\right)-5
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
5x^{2}+10x+5+3\left(x+1\right)-5
Use the distributive property to multiply 5 by x^{2}+2x+1.
5x^{2}+10x+5+3x+3-5
Use the distributive property to multiply 3 by x+1.
5x^{2}+13x+5+3-5
Combine 10x and 3x to get 13x.
5x^{2}+13x+8-5
Add 5 and 3 to get 8.
5x^{2}+13x+3
Subtract 5 from 8 to get 3.
5\left(x^{2}+2x+1\right)+3\left(x+1\right)-5
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.
5x^{2}+10x+5+3\left(x+1\right)-5
Use the distributive property to multiply 5 by x^{2}+2x+1.
5x^{2}+10x+5+3x+3-5
Use the distributive property to multiply 3 by x+1.
5x^{2}+13x+5+3-5
Combine 10x and 3x to get 13x.
5x^{2}+13x+8-5
Add 5 and 3 to get 8.
5x^{2}+13x+3
Subtract 5 from 8 to get 3.
Examples
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}