Evaluate
\left(2x+1\right)\left(8x+1\right)\left(8x+7\right)
Expand
128x^{3}+192x^{2}+78x+7
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16\left(8x^{3}+12x^{2}+6x+1\right)-9\left(2x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x+1\right)^{3}.
128x^{3}+192x^{2}+96x+16-9\left(2x+1\right)
Use the distributive property to multiply 16 by 8x^{3}+12x^{2}+6x+1.
128x^{3}+192x^{2}+96x+16-18x-9
Use the distributive property to multiply -9 by 2x+1.
128x^{3}+192x^{2}+78x+16-9
Combine 96x and -18x to get 78x.
128x^{3}+192x^{2}+78x+7
Subtract 9 from 16 to get 7.
16\left(8x^{3}+12x^{2}+6x+1\right)-9\left(2x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x+1\right)^{3}.
128x^{3}+192x^{2}+96x+16-9\left(2x+1\right)
Use the distributive property to multiply 16 by 8x^{3}+12x^{2}+6x+1.
128x^{3}+192x^{2}+96x+16-18x-9
Use the distributive property to multiply -9 by 2x+1.
128x^{3}+192x^{2}+78x+16-9
Combine 96x and -18x to get 78x.
128x^{3}+192x^{2}+78x+7
Subtract 9 from 16 to get 7.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}