Factor
\frac{\left(3x+1\right)\left(6x+1\right)}{18}
Evaluate
x^{2}+\frac{x}{2}+\frac{1}{18}
Graph
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\frac{18x^{2}+9x+1}{18}
Factor out \frac{1}{18}.
a+b=9 ab=18\times 1=18
Consider 18x^{2}+9x+1. Factor the expression by grouping. First, the expression needs to be rewritten as 18x^{2}+ax+bx+1. To find a and b, set up a system to be solved.
1,18 2,9 3,6
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 18.
1+18=19 2+9=11 3+6=9
Calculate the sum for each pair.
a=3 b=6
The solution is the pair that gives sum 9.
\left(18x^{2}+3x\right)+\left(6x+1\right)
Rewrite 18x^{2}+9x+1 as \left(18x^{2}+3x\right)+\left(6x+1\right).
3x\left(6x+1\right)+6x+1
Factor out 3x in 18x^{2}+3x.
\left(6x+1\right)\left(3x+1\right)
Factor out common term 6x+1 by using distributive property.
\frac{\left(6x+1\right)\left(3x+1\right)}{18}
Rewrite the complete factored expression.
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
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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}