Evaluate
\left(4x-3\right)\left(5x-3\right)^{3}-x
Expand
500x^{4}-1275x^{3}+1215x^{2}-514x+81
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\left(5x-3\right)^{3}\left(4x-3\right)-x
Combine 4x and x to get 5x.
\left(125x^{3}-225x^{2}+135x-27\right)\left(4x-3\right)-x
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5x-3\right)^{3}.
500x^{4}-1275x^{3}+1215x^{2}-513x+81-x
Use the distributive property to multiply 125x^{3}-225x^{2}+135x-27 by 4x-3 and combine like terms.
500x^{4}-1275x^{3}+1215x^{2}-514x+81
Combine -513x and -x to get -514x.
\left(5x-3\right)^{3}\left(4x-3\right)-x
Combine 4x and x to get 5x.
\left(125x^{3}-225x^{2}+135x-27\right)\left(4x-3\right)-x
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(5x-3\right)^{3}.
500x^{4}-1275x^{3}+1215x^{2}-513x+81-x
Use the distributive property to multiply 125x^{3}-225x^{2}+135x-27 by 4x-3 and combine like terms.
500x^{4}-1275x^{3}+1215x^{2}-514x+81
Combine -513x and -x to get -514x.
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}