Evaluate
\left(1-y\right)^{3}
Expand
1-3y+3y^{2}-y^{3}
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\left(-y\right)^{3}+3\left(-y\right)^{2}+3\left(-y\right)+1
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(-y+1\right)^{3}.
\left(-y\right)^{3}+3y^{2}+3\left(-y\right)+1
Calculate -y to the power of 2 and get y^{2}.
\left(-1\right)^{3}y^{3}+3y^{2}+3\left(-1\right)y+1
Expand \left(-y\right)^{3}.
-y^{3}+3y^{2}+3\left(-1\right)y+1
Calculate -1 to the power of 3 and get -1.
-y^{3}+3y^{2}-3y+1
Multiply 3 and -1 to get -3.
\left(-y\right)^{3}+3\left(-y\right)^{2}+3\left(-y\right)+1
Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(-y+1\right)^{3}.
\left(-y\right)^{3}+3y^{2}+3\left(-y\right)+1
Calculate -y to the power of 2 and get y^{2}.
\left(-1\right)^{3}y^{3}+3y^{2}+3\left(-1\right)y+1
Expand \left(-y\right)^{3}.
-y^{3}+3y^{2}+3\left(-1\right)y+1
Calculate -1 to the power of 3 and get -1.
-y^{3}+3y^{2}-3y+1
Multiply 3 and -1 to get -3.
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
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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}