Evaluate
2\left(3\alpha -1\right)\left(\beta +4\right)
Expand
6\alpha \beta +24\alpha -2\beta -8
Share
Copied to clipboard
3\alpha \beta +9\alpha -\beta -3-\left(1-3\alpha \right)\left(\beta +5\right)
Apply the distributive property by multiplying each term of 3\alpha -1 by each term of \beta +3.
3\alpha \beta +9\alpha -\beta -3-\left(\beta +5-3\alpha \beta -15\alpha \right)
Apply the distributive property by multiplying each term of 1-3\alpha by each term of \beta +5.
3\alpha \beta +9\alpha -\beta -3-\beta -5-\left(-3\alpha \beta \right)-\left(-15\alpha \right)
To find the opposite of \beta +5-3\alpha \beta -15\alpha , find the opposite of each term.
3\alpha \beta +9\alpha -\beta -3-\beta -5+3\alpha \beta -\left(-15\alpha \right)
The opposite of -3\alpha \beta is 3\alpha \beta .
3\alpha \beta +9\alpha -\beta -3-\beta -5+3\alpha \beta +15\alpha
The opposite of -15\alpha is 15\alpha .
3\alpha \beta +9\alpha -2\beta -3-5+3\alpha \beta +15\alpha
Combine -\beta and -\beta to get -2\beta .
3\alpha \beta +9\alpha -2\beta -8+3\alpha \beta +15\alpha
Subtract 5 from -3 to get -8.
6\alpha \beta +9\alpha -2\beta -8+15\alpha
Combine 3\alpha \beta and 3\alpha \beta to get 6\alpha \beta .
6\alpha \beta +24\alpha -2\beta -8
Combine 9\alpha and 15\alpha to get 24\alpha .
3\alpha \beta +9\alpha -\beta -3-\left(1-3\alpha \right)\left(\beta +5\right)
Apply the distributive property by multiplying each term of 3\alpha -1 by each term of \beta +3.
3\alpha \beta +9\alpha -\beta -3-\left(\beta +5-3\alpha \beta -15\alpha \right)
Apply the distributive property by multiplying each term of 1-3\alpha by each term of \beta +5.
3\alpha \beta +9\alpha -\beta -3-\beta -5-\left(-3\alpha \beta \right)-\left(-15\alpha \right)
To find the opposite of \beta +5-3\alpha \beta -15\alpha , find the opposite of each term.
3\alpha \beta +9\alpha -\beta -3-\beta -5+3\alpha \beta -\left(-15\alpha \right)
The opposite of -3\alpha \beta is 3\alpha \beta .
3\alpha \beta +9\alpha -\beta -3-\beta -5+3\alpha \beta +15\alpha
The opposite of -15\alpha is 15\alpha .
3\alpha \beta +9\alpha -2\beta -3-5+3\alpha \beta +15\alpha
Combine -\beta and -\beta to get -2\beta .
3\alpha \beta +9\alpha -2\beta -8+3\alpha \beta +15\alpha
Subtract 5 from -3 to get -8.
6\alpha \beta +9\alpha -2\beta -8+15\alpha
Combine 3\alpha \beta and 3\alpha \beta to get 6\alpha \beta .
6\alpha \beta +24\alpha -2\beta -8
Combine 9\alpha and 15\alpha to get 24\alpha .
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}