Evaluate
24x\left(10x-1\right)
Expand
240x^{2}-24x
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20x-3+100x^{2}+\left(10x-1\right)^{2}+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Subtract 1 from -2 to get -3.
20x-3+100x^{2}+100x^{2}-20x+1+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10x-1\right)^{2}.
20x-3+200x^{2}-20x+1+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Combine 100x^{2} and 100x^{2} to get 200x^{2}.
-3+200x^{2}+1+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Combine 20x and -20x to get 0.
-2+200x^{2}+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Add -3 and 1 to get -2.
-2+200x^{2}+20x^{2}-2x+\left(2x-2\right)\left(10x-1\right)
Use the distributive property to multiply 2x by 10x-1.
-2+220x^{2}-2x+\left(2x-2\right)\left(10x-1\right)
Combine 200x^{2} and 20x^{2} to get 220x^{2}.
-2+220x^{2}-2x+20x^{2}-22x+2
Use the distributive property to multiply 2x-2 by 10x-1 and combine like terms.
-2+240x^{2}-2x-22x+2
Combine 220x^{2} and 20x^{2} to get 240x^{2}.
-2+240x^{2}-24x+2
Combine -2x and -22x to get -24x.
240x^{2}-24x
Add -2 and 2 to get 0.
20x-3+100x^{2}+\left(10x-1\right)^{2}+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Subtract 1 from -2 to get -3.
20x-3+100x^{2}+100x^{2}-20x+1+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10x-1\right)^{2}.
20x-3+200x^{2}-20x+1+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Combine 100x^{2} and 100x^{2} to get 200x^{2}.
-3+200x^{2}+1+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Combine 20x and -20x to get 0.
-2+200x^{2}+2x\left(10x-1\right)+\left(2x-2\right)\left(10x-1\right)
Add -3 and 1 to get -2.
-2+200x^{2}+20x^{2}-2x+\left(2x-2\right)\left(10x-1\right)
Use the distributive property to multiply 2x by 10x-1.
-2+220x^{2}-2x+\left(2x-2\right)\left(10x-1\right)
Combine 200x^{2} and 20x^{2} to get 220x^{2}.
-2+220x^{2}-2x+20x^{2}-22x+2
Use the distributive property to multiply 2x-2 by 10x-1 and combine like terms.
-2+240x^{2}-2x-22x+2
Combine 220x^{2} and 20x^{2} to get 240x^{2}.
-2+240x^{2}-24x+2
Combine -2x and -22x to get -24x.
240x^{2}-24x
Add -2 and 2 to get 0.
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}