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9x^{2}-43x+41
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9x^{2}-43x+41
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4x^{2}-20x+25+\left(3x-3\right)^{2}-4x^{2}-5x+7
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.
4x^{2}-20x+25+9x^{2}-18x+9-4x^{2}-5x+7
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-3\right)^{2}.
13x^{2}-20x+25-18x+9-4x^{2}-5x+7
Combine 4x^{2} and 9x^{2} to get 13x^{2}.
13x^{2}-38x+25+9-4x^{2}-5x+7
Combine -20x and -18x to get -38x.
13x^{2}-38x+34-4x^{2}-5x+7
Add 25 and 9 to get 34.
9x^{2}-38x+34-5x+7
Combine 13x^{2} and -4x^{2} to get 9x^{2}.
9x^{2}-43x+34+7
Combine -38x and -5x to get -43x.
9x^{2}-43x+41
Add 34 and 7 to get 41.
4x^{2}-20x+25+\left(3x-3\right)^{2}-4x^{2}-5x+7
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.
4x^{2}-20x+25+9x^{2}-18x+9-4x^{2}-5x+7
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-3\right)^{2}.
13x^{2}-20x+25-18x+9-4x^{2}-5x+7
Combine 4x^{2} and 9x^{2} to get 13x^{2}.
13x^{2}-38x+25+9-4x^{2}-5x+7
Combine -20x and -18x to get -38x.
13x^{2}-38x+34-4x^{2}-5x+7
Add 25 and 9 to get 34.
9x^{2}-38x+34-5x+7
Combine 13x^{2} and -4x^{2} to get 9x^{2}.
9x^{2}-43x+34+7
Combine -38x and -5x to get -43x.
9x^{2}-43x+41
Add 34 and 7 to get 41.
Examples
Quadratic equation
{ 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}