Factor
2x\left(x+1\right)\left(x+7\right)
Evaluate
2x\left(x+1\right)\left(x+7\right)
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2\left(x^{3}+8x^{2}+7x\right)
Factor out 2.
x\left(x^{2}+8x+7\right)
Consider x^{3}+8x^{2}+7x. Factor out x.
a+b=8 ab=1\times 7=7
Consider x^{2}+8x+7. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+7. To find a and b, set up a system to be solved.
a=1 b=7
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.
\left(x^{2}+x\right)+\left(7x+7\right)
Rewrite x^{2}+8x+7 as \left(x^{2}+x\right)+\left(7x+7\right).
x\left(x+1\right)+7\left(x+1\right)
Factor out x in the first and 7 in the second group.
\left(x+1\right)\left(x+7\right)
Factor out common term x+1 by using distributive property.
2x\left(x+1\right)\left(x+7\right)
Rewrite the complete factored expression.
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
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Limits
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