Evaluate
-\left(a-2\right)\left(a+3\right)
Expand
6-a-a^{2}
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\left(-\frac{1}{2}a-\left(-1\right)\right)\left(2a+6\right)
To find the opposite of \frac{1}{2}a-1, find the opposite of each term.
\left(-\frac{1}{2}a+1\right)\left(2a+6\right)
The opposite of -1 is 1.
-\frac{1}{2}a\times 2a-\frac{1}{2}a\times 6+2a+6
Apply the distributive property by multiplying each term of -\frac{1}{2}a+1 by each term of 2a+6.
-\frac{1}{2}a^{2}\times 2-\frac{1}{2}a\times 6+2a+6
Multiply a and a to get a^{2}.
-a^{2}-\frac{1}{2}a\times 6+2a+6
Cancel out 2 and 2.
-a^{2}+\frac{-6}{2}a+2a+6
Express -\frac{1}{2}\times 6 as a single fraction.
-a^{2}-3a+2a+6
Divide -6 by 2 to get -3.
-a^{2}-a+6
Combine -3a and 2a to get -a.
\left(-\frac{1}{2}a-\left(-1\right)\right)\left(2a+6\right)
To find the opposite of \frac{1}{2}a-1, find the opposite of each term.
\left(-\frac{1}{2}a+1\right)\left(2a+6\right)
The opposite of -1 is 1.
-\frac{1}{2}a\times 2a-\frac{1}{2}a\times 6+2a+6
Apply the distributive property by multiplying each term of -\frac{1}{2}a+1 by each term of 2a+6.
-\frac{1}{2}a^{2}\times 2-\frac{1}{2}a\times 6+2a+6
Multiply a and a to get a^{2}.
-a^{2}-\frac{1}{2}a\times 6+2a+6
Cancel out 2 and 2.
-a^{2}+\frac{-6}{2}a+2a+6
Express -\frac{1}{2}\times 6 as a single fraction.
-a^{2}-3a+2a+6
Divide -6 by 2 to get -3.
-a^{2}-a+6
Combine -3a and 2a to get -a.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}