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3A^{2}-4A+9
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3A^{2}-4A+9
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3\left(1-2A+A^{2}\right)-2\left(1-A\right)+8
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-A\right)^{2}.
3-6A+3A^{2}-2\left(1-A\right)+8
Use the distributive property to multiply 3 by 1-2A+A^{2}.
3-6A+3A^{2}-2+2A+8
Use the distributive property to multiply -2 by 1-A.
1-6A+3A^{2}+2A+8
Subtract 2 from 3 to get 1.
1-4A+3A^{2}+8
Combine -6A and 2A to get -4A.
9-4A+3A^{2}
Add 1 and 8 to get 9.
3\left(1-2A+A^{2}\right)-2\left(1-A\right)+8
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-A\right)^{2}.
3-6A+3A^{2}-2\left(1-A\right)+8
Use the distributive property to multiply 3 by 1-2A+A^{2}.
3-6A+3A^{2}-2+2A+8
Use the distributive property to multiply -2 by 1-A.
1-6A+3A^{2}+2A+8
Subtract 2 from 3 to get 1.
1-4A+3A^{2}+8
Combine -6A and 2A to get -4A.
9-4A+3A^{2}
Add 1 and 8 to get 9.
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}