Factor
5\left(x-1\right)\left(5x-1\right)x^{2}
Evaluate
5\left(x-1\right)\left(5x-1\right)x^{2}
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5\left(5x^{4}-6x^{3}+x^{2}\right)
Factor out 5.
x^{2}\left(5x^{2}-6x+1\right)
Consider 5x^{4}-6x^{3}+x^{2}. Factor out x^{2}.
a+b=-6 ab=5\times 1=5
Consider 5x^{2}-6x+1. Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx+1. To find a and b, set up a system to be solved.
a=-5 b=-1
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.
\left(5x^{2}-5x\right)+\left(-x+1\right)
Rewrite 5x^{2}-6x+1 as \left(5x^{2}-5x\right)+\left(-x+1\right).
5x\left(x-1\right)-\left(x-1\right)
Factor out 5x in the first and -1 in the second group.
\left(x-1\right)\left(5x-1\right)
Factor out common term x-1 by using distributive property.
5x^{2}\left(x-1\right)\left(5x-1\right)
Rewrite the complete factored expression.
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}