Evaluate
-5n^{2}+11n-8
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-5n^{2}+11n-8
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n^{2}-2^{2}+\left(3n-4\right)\left(1-2n\right)
Consider \left(n+2\right)\left(n-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
n^{2}-4+\left(3n-4\right)\left(1-2n\right)
Calculate 2 to the power of 2 and get 4.
n^{2}-4+3n-6n^{2}-4+8n
Apply the distributive property by multiplying each term of 3n-4 by each term of 1-2n.
n^{2}-4+11n-6n^{2}-4
Combine 3n and 8n to get 11n.
-5n^{2}-4+11n-4
Combine n^{2} and -6n^{2} to get -5n^{2}.
-5n^{2}-8+11n
Subtract 4 from -4 to get -8.
n^{2}-2^{2}+\left(3n-4\right)\left(1-2n\right)
Consider \left(n+2\right)\left(n-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
n^{2}-4+\left(3n-4\right)\left(1-2n\right)
Calculate 2 to the power of 2 and get 4.
n^{2}-4+3n-6n^{2}-4+8n
Apply the distributive property by multiplying each term of 3n-4 by each term of 1-2n.
n^{2}-4+11n-6n^{2}-4
Combine 3n and 8n to get 11n.
-5n^{2}-4+11n-4
Combine n^{2} and -6n^{2} to get -5n^{2}.
-5n^{2}-8+11n
Subtract 4 from -4 to get -8.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}