Evaluate
\left(2x-3\right)\left(\left(2x-3\right)^{2}-5\right)
Expand
8x^{3}-36x^{2}+44x-12
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8x^{3}-36x^{2}+54x-27-5\left(2x-3\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-3\right)^{3}.
8x^{3}-36x^{2}+54x-27-10x+15
Use the distributive property to multiply -5 by 2x-3.
8x^{3}-36x^{2}+44x-27+15
Combine 54x and -10x to get 44x.
8x^{3}-36x^{2}+44x-12
Add -27 and 15 to get -12.
8x^{3}-36x^{2}+54x-27-5\left(2x-3\right)
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2x-3\right)^{3}.
8x^{3}-36x^{2}+54x-27-10x+15
Use the distributive property to multiply -5 by 2x-3.
8x^{3}-36x^{2}+44x-27+15
Combine 54x and -10x to get 44x.
8x^{3}-36x^{2}+44x-12
Add -27 and 15 to get -12.
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}