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13x^{2}-42x+34
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13x^{2}-42x+34
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4x^{2}-12x+9+\left(3x-5\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.
4x^{2}-12x+9+9x^{2}-30x+25
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-5\right)^{2}.
13x^{2}-12x+9-30x+25
Combine 4x^{2} and 9x^{2} to get 13x^{2}.
13x^{2}-42x+9+25
Combine -12x and -30x to get -42x.
13x^{2}-42x+34
Add 9 and 25 to get 34.
4x^{2}-12x+9+\left(3x-5\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.
4x^{2}-12x+9+9x^{2}-30x+25
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-5\right)^{2}.
13x^{2}-12x+9-30x+25
Combine 4x^{2} and 9x^{2} to get 13x^{2}.
13x^{2}-42x+9+25
Combine -12x and -30x to get -42x.
13x^{2}-42x+34
Add 9 and 25 to get 34.
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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}