Factor
\left(x+2\right)\left(5x+2\right)
Evaluate
\left(x+2\right)\left(5x+2\right)
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5x^{2}+12x+4
Multiply and combine like terms.
a+b=12 ab=5\times 4=20
Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx+4. To find a and b, set up a system to be solved.
1,20 2,10 4,5
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 20.
1+20=21 2+10=12 4+5=9
Calculate the sum for each pair.
a=2 b=10
The solution is the pair that gives sum 12.
\left(5x^{2}+2x\right)+\left(10x+4\right)
Rewrite 5x^{2}+12x+4 as \left(5x^{2}+2x\right)+\left(10x+4\right).
x\left(5x+2\right)+2\left(5x+2\right)
Factor out x in the first and 2 in the second group.
\left(5x+2\right)\left(x+2\right)
Factor out common term 5x+2 by using distributive property.
5x^{2}+12x+4
Combine 2x and 10x to get 12x.
Examples
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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
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