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-6x^{2}-2
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-6x^{2}-2
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x^{3}-3x^{2}+3x-1-\left(x+1\right)^{3}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.
x^{3}-3x^{2}+3x-1-\left(x^{3}+3x^{2}+3x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
x^{3}-3x^{2}+3x-1-x^{3}-3x^{2}-3x-1
To find the opposite of x^{3}+3x^{2}+3x+1, find the opposite of each term.
-3x^{2}+3x-1-3x^{2}-3x-1
Combine x^{3} and -x^{3} to get 0.
-6x^{2}+3x-1-3x-1
Combine -3x^{2} and -3x^{2} to get -6x^{2}.
-6x^{2}-1-1
Combine 3x and -3x to get 0.
-6x^{2}-2
Subtract 1 from -1 to get -2.
x^{3}-3x^{2}+3x-1-\left(x+1\right)^{3}
Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.
x^{3}-3x^{2}+3x-1-\left(x^{3}+3x^{2}+3x+1\right)
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.
x^{3}-3x^{2}+3x-1-x^{3}-3x^{2}-3x-1
To find the opposite of x^{3}+3x^{2}+3x+1, find the opposite of each term.
-3x^{2}+3x-1-3x^{2}-3x-1
Combine x^{3} and -x^{3} to get 0.
-6x^{2}+3x-1-3x-1
Combine -3x^{2} and -3x^{2} to get -6x^{2}.
-6x^{2}-1-1
Combine 3x and -3x to get 0.
-6x^{2}-2
Subtract 1 from -1 to get -2.
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y = 3x + 4
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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}