Evaluate
x\left(x+2y-2\right)
Expand
x^{2}+2xy-2x
Share
Copied to clipboard
x^{2}+2xy-2x+y^{2}-2y+1-\left(y-1\right)^{2}
Square x+y-1.
x^{2}+2xy-2x+y^{2}-2y+1-\left(y^{2}-2y+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-1\right)^{2}.
x^{2}+2xy-2x+y^{2}-2y+1-y^{2}+2y-1
To find the opposite of y^{2}-2y+1, find the opposite of each term.
x^{2}+2xy-2x-2y+1+2y-1
Combine y^{2} and -y^{2} to get 0.
x^{2}+2xy-2x+1-1
Combine -2y and 2y to get 0.
x^{2}+2xy-2x
Subtract 1 from 1 to get 0.
x^{2}+2xy-2x+y^{2}-2y+1-\left(y-1\right)^{2}
Square x+y-1.
x^{2}+2xy-2x+y^{2}-2y+1-\left(y^{2}-2y+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-1\right)^{2}.
x^{2}+2xy-2x+y^{2}-2y+1-y^{2}+2y-1
To find the opposite of y^{2}-2y+1, find the opposite of each term.
x^{2}+2xy-2x-2y+1+2y-1
Combine y^{2} and -y^{2} to get 0.
x^{2}+2xy-2x+1-1
Combine -2y and 2y to get 0.
x^{2}+2xy-2x
Subtract 1 from 1 to get 0.
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}