Evaluate
\frac{2\left(16-9x\right)\left(x-2\right)}{15}
Expand
-\frac{6x^{2}}{5}+\frac{68x}{15}-\frac{64}{15}
Graph
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\left(2x-4\right)\left(\frac{3\left(7x+2\right)}{15}+\frac{5\times 2\left(1-3x\right)}{15}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{7x+2}{5} times \frac{3}{3}. Multiply \frac{2\left(1-3x\right)}{3} times \frac{5}{5}.
\left(2x-4\right)\times \frac{3\left(7x+2\right)+5\times 2\left(1-3x\right)}{15}
Since \frac{3\left(7x+2\right)}{15} and \frac{5\times 2\left(1-3x\right)}{15} have the same denominator, add them by adding their numerators.
\left(2x-4\right)\times \frac{21x+6+10-30x}{15}
Do the multiplications in 3\left(7x+2\right)+5\times 2\left(1-3x\right).
\left(2x-4\right)\times \frac{-9x+16}{15}
Combine like terms in 21x+6+10-30x.
\frac{\left(2x-4\right)\left(-9x+16\right)}{15}
Express \left(2x-4\right)\times \frac{-9x+16}{15} as a single fraction.
\frac{-18x^{2}+32x+36x-64}{15}
Apply the distributive property by multiplying each term of 2x-4 by each term of -9x+16.
\frac{-18x^{2}+68x-64}{15}
Combine 32x and 36x to get 68x.
\left(2x-4\right)\left(\frac{3\left(7x+2\right)}{15}+\frac{5\times 2\left(1-3x\right)}{15}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{7x+2}{5} times \frac{3}{3}. Multiply \frac{2\left(1-3x\right)}{3} times \frac{5}{5}.
\left(2x-4\right)\times \frac{3\left(7x+2\right)+5\times 2\left(1-3x\right)}{15}
Since \frac{3\left(7x+2\right)}{15} and \frac{5\times 2\left(1-3x\right)}{15} have the same denominator, add them by adding their numerators.
\left(2x-4\right)\times \frac{21x+6+10-30x}{15}
Do the multiplications in 3\left(7x+2\right)+5\times 2\left(1-3x\right).
\left(2x-4\right)\times \frac{-9x+16}{15}
Combine like terms in 21x+6+10-30x.
\frac{\left(2x-4\right)\left(-9x+16\right)}{15}
Express \left(2x-4\right)\times \frac{-9x+16}{15} as a single fraction.
\frac{-18x^{2}+32x+36x-64}{15}
Apply the distributive property by multiplying each term of 2x-4 by each term of -9x+16.
\frac{-18x^{2}+68x-64}{15}
Combine 32x and 36x to get 68x.
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}