Evaluate
\left(x-5\right)\left(x+3\right)^{2}
Expand
x^{3}+x^{2}-21x-45
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\left(x-5\right)\left(x+3\right)^{2}
Multiply x+3 and x+3 to get \left(x+3\right)^{2}.
\left(x-5\right)\left(x^{2}+6x+9\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
x^{3}+6x^{2}+9x-5x^{2}-30x-45
Apply the distributive property by multiplying each term of x-5 by each term of x^{2}+6x+9.
x^{3}+x^{2}+9x-30x-45
Combine 6x^{2} and -5x^{2} to get x^{2}.
x^{3}+x^{2}-21x-45
Combine 9x and -30x to get -21x.
\left(x-5\right)\left(x+3\right)^{2}
Multiply x+3 and x+3 to get \left(x+3\right)^{2}.
\left(x-5\right)\left(x^{2}+6x+9\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
x^{3}+6x^{2}+9x-5x^{2}-30x-45
Apply the distributive property by multiplying each term of x-5 by each term of x^{2}+6x+9.
x^{3}+x^{2}+9x-30x-45
Combine 6x^{2} and -5x^{2} to get x^{2}.
x^{3}+x^{2}-21x-45
Combine 9x and -30x to get -21x.
Examples
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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}