Evaluate
2\left(\left(x+1\right)^{2}-42\right)
Expand
2x^{2}+4x-82
Graph
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2\left(1+2x+x^{2}\right)-2\times 42
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x\right)^{2}.
2+4x+2x^{2}-2\times 42
Use the distributive property to multiply 2 by 1+2x+x^{2}.
2+4x+2x^{2}-84
Multiply 2 and 42 to get 84.
-82+4x+2x^{2}
Subtract 84 from 2 to get -82.
2\left(1+2x+x^{2}\right)-2\times 42
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x\right)^{2}.
2+4x+2x^{2}-2\times 42
Use the distributive property to multiply 2 by 1+2x+x^{2}.
2+4x+2x^{2}-84
Multiply 2 and 42 to get 84.
-82+4x+2x^{2}
Subtract 84 from 2 to get -82.
Examples
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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
699 * 533
Matrix
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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
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