Evaluate
\left(x^{2}+x-1\right)^{2}
Expand
x^{4}+2x^{3}-x^{2}-2x+1
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\left(x^{2}\right)^{2}+2x^{2}x+x^{2}-2\left(x^{2}+x\right)+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+x\right)^{2}.
x^{4}+2x^{2}x+x^{2}-2\left(x^{2}+x\right)+1
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
x^{4}+2x^{3}+x^{2}-2\left(x^{2}+x\right)+1
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{4}+2x^{3}+x^{2}-2x^{2}-2x+1
Use the distributive property to multiply -2 by x^{2}+x.
x^{4}+2x^{3}-x^{2}-2x+1
Combine x^{2} and -2x^{2} to get -x^{2}.
\left(x^{2}\right)^{2}+2x^{2}x+x^{2}-2\left(x^{2}+x\right)+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x^{2}+x\right)^{2}.
x^{4}+2x^{2}x+x^{2}-2\left(x^{2}+x\right)+1
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
x^{4}+2x^{3}+x^{2}-2\left(x^{2}+x\right)+1
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{4}+2x^{3}+x^{2}-2x^{2}-2x+1
Use the distributive property to multiply -2 by x^{2}+x.
x^{4}+2x^{3}-x^{2}-2x+1
Combine x^{2} and -2x^{2} to get -x^{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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Linear equation
y = 3x + 4
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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}