Evaluate
x^{4}-2x^{3}-\frac{53x^{2}}{3}+10x+\frac{40}{3}
Expand
x^{4}-2x^{3}-\frac{53x^{2}}{3}+10x+\frac{40}{3}
Graph
Share
Copied to clipboard
x^{4}-2x^{3}-11x^{2}+30x-\frac{20\left(x^{2}+3x-2\right)}{3}
Express 20\times \frac{x^{2}+3x-2}{3} as a single fraction.
x^{4}-2x^{3}-11x^{2}+30x-\frac{20x^{2}+60x-40}{3}
Use the distributive property to multiply 20 by x^{2}+3x-2.
\frac{3\left(x^{4}-2x^{3}-11x^{2}+30x\right)}{3}-\frac{20x^{2}+60x-40}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4}-2x^{3}-11x^{2}+30x times \frac{3}{3}.
\frac{3\left(x^{4}-2x^{3}-11x^{2}+30x\right)-\left(20x^{2}+60x-40\right)}{3}
Since \frac{3\left(x^{4}-2x^{3}-11x^{2}+30x\right)}{3} and \frac{20x^{2}+60x-40}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{4}-6x^{3}-33x^{2}+90x-20x^{2}-60x+40}{3}
Do the multiplications in 3\left(x^{4}-2x^{3}-11x^{2}+30x\right)-\left(20x^{2}+60x-40\right).
\frac{3x^{4}-6x^{3}-53x^{2}+30x+40}{3}
Combine like terms in 3x^{4}-6x^{3}-33x^{2}+90x-20x^{2}-60x+40.
x^{4}-2x^{3}-11x^{2}+30x-\frac{20\left(x^{2}+3x-2\right)}{3}
Express 20\times \frac{x^{2}+3x-2}{3} as a single fraction.
x^{4}-2x^{3}-11x^{2}+30x-\frac{20x^{2}+60x-40}{3}
Use the distributive property to multiply 20 by x^{2}+3x-2.
\frac{3\left(x^{4}-2x^{3}-11x^{2}+30x\right)}{3}-\frac{20x^{2}+60x-40}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4}-2x^{3}-11x^{2}+30x times \frac{3}{3}.
\frac{3\left(x^{4}-2x^{3}-11x^{2}+30x\right)-\left(20x^{2}+60x-40\right)}{3}
Since \frac{3\left(x^{4}-2x^{3}-11x^{2}+30x\right)}{3} and \frac{20x^{2}+60x-40}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{4}-6x^{3}-33x^{2}+90x-20x^{2}-60x+40}{3}
Do the multiplications in 3\left(x^{4}-2x^{3}-11x^{2}+30x\right)-\left(20x^{2}+60x-40\right).
\frac{3x^{4}-6x^{3}-53x^{2}+30x+40}{3}
Combine like terms in 3x^{4}-6x^{3}-33x^{2}+90x-20x^{2}-60x+40.
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}