Evaluate
-\left(x-4\right)\left(1-x\right)^{2}
Expand
4-9x+6x^{2}-x^{3}
Graph
Share
Copied to clipboard
x^{2}\left(-x\right)+x^{2}-5x\left(-x\right)-5x+4\left(-x\right)+4
Use the distributive property to multiply x^{2}-5x+4 by -x+1.
x^{2}\left(-x\right)+x^{2}+5xx-5x+4\left(-x\right)+4
Multiply -5 and -1 to get 5.
x^{2}\left(-x\right)+x^{2}+5x^{2}-5x+4\left(-x\right)+4
Multiply x and x to get x^{2}.
x^{2}\left(-x\right)+6x^{2}-5x+4\left(-x\right)+4
Combine x^{2} and 5x^{2} to get 6x^{2}.
x^{3}\left(-1\right)+6x^{2}-5x+4\left(-1\right)x+4
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{3}\left(-1\right)+6x^{2}-5x-4x+4
Multiply 4 and -1 to get -4.
x^{3}\left(-1\right)+6x^{2}-9x+4
Combine -5x and -4x to get -9x.
x^{2}\left(-x\right)+x^{2}-5x\left(-x\right)-5x+4\left(-x\right)+4
Use the distributive property to multiply x^{2}-5x+4 by -x+1.
x^{2}\left(-x\right)+x^{2}+5xx-5x+4\left(-x\right)+4
Multiply -5 and -1 to get 5.
x^{2}\left(-x\right)+x^{2}+5x^{2}-5x+4\left(-x\right)+4
Multiply x and x to get x^{2}.
x^{2}\left(-x\right)+6x^{2}-5x+4\left(-x\right)+4
Combine x^{2} and 5x^{2} to get 6x^{2}.
x^{3}\left(-1\right)+6x^{2}-5x+4\left(-1\right)x+4
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{3}\left(-1\right)+6x^{2}-5x-4x+4
Multiply 4 and -1 to get -4.
x^{3}\left(-1\right)+6x^{2}-9x+4
Combine -5x and -4x to get -9x.
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}