Evaluate
\left(x-3\right)\left(x-2\right)^{2}
Expand
x^{3}-7x^{2}+16x-12
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\left(x-2\right)^{2}\left(x-3\right)
Multiply x-2 and x-2 to get \left(x-2\right)^{2}.
\left(x^{2}-4x+4\right)\left(x-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{3}-3x^{2}-4x^{2}+12x+4x-12
Apply the distributive property by multiplying each term of x^{2}-4x+4 by each term of x-3.
x^{3}-7x^{2}+12x+4x-12
Combine -3x^{2} and -4x^{2} to get -7x^{2}.
x^{3}-7x^{2}+16x-12
Combine 12x and 4x to get 16x.
\left(x-2\right)^{2}\left(x-3\right)
Multiply x-2 and x-2 to get \left(x-2\right)^{2}.
\left(x^{2}-4x+4\right)\left(x-3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{3}-3x^{2}-4x^{2}+12x+4x-12
Apply the distributive property by multiplying each term of x^{2}-4x+4 by each term of x-3.
x^{3}-7x^{2}+12x+4x-12
Combine -3x^{2} and -4x^{2} to get -7x^{2}.
x^{3}-7x^{2}+16x-12
Combine 12x and 4x to get 16x.
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
\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}