Evaluate
\left(t+12\right)\left(2t+3\right)
Expand
2t^{2}+27t+36
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\left(3t+9\right)\left(2t+3\right)-\left(4t^{2}-9\right)
Use the distributive property to multiply 3 by t+3.
6t^{2}+27t+27-\left(4t^{2}-9\right)
Use the distributive property to multiply 3t+9 by 2t+3 and combine like terms.
6t^{2}+27t+27-4t^{2}+9
To find the opposite of 4t^{2}-9, find the opposite of each term.
2t^{2}+27t+27+9
Combine 6t^{2} and -4t^{2} to get 2t^{2}.
2t^{2}+27t+36
Add 27 and 9 to get 36.
\left(3t+9\right)\left(2t+3\right)-\left(4t^{2}-9\right)
Use the distributive property to multiply 3 by t+3.
6t^{2}+27t+27-\left(4t^{2}-9\right)
Use the distributive property to multiply 3t+9 by 2t+3 and combine like terms.
6t^{2}+27t+27-4t^{2}+9
To find the opposite of 4t^{2}-9, find the opposite of each term.
2t^{2}+27t+27+9
Combine 6t^{2} and -4t^{2} to get 2t^{2}.
2t^{2}+27t+36
Add 27 and 9 to get 36.
Examples
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{ 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}