Evaluate
-x^{8}+x^{5}+\left(x+40\right)^{2}+x+12y_{5}-6215
Expand
-x^{8}+x^{5}+x^{2}+81x+12y_{5}-4615
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x^{5}+x+\left(40+x\right)^{2}-x^{8}-6215+12y_{5}
To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.
x^{5}+x+1600+80x+x^{2}-x^{8}-6215+12y_{5}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(40+x\right)^{2}.
x^{5}+81x+1600+x^{2}-x^{8}-6215+12y_{5}
Combine x and 80x to get 81x.
x^{5}+81x-4615+x^{2}-x^{8}+12y_{5}
Subtract 6215 from 1600 to get -4615.
x^{5}+x+\left(40+x\right)^{2}-x^{8}-6215+12y_{5}
To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.
x^{5}+x+1600+80x+x^{2}-x^{8}-6215+12y_{5}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(40+x\right)^{2}.
x^{5}+81x+1600+x^{2}-x^{8}-6215+12y_{5}
Combine x and 80x to get 81x.
x^{5}+81x-4615+x^{2}-x^{8}+12y_{5}
Subtract 6215 from 1600 to get -4615.
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}