What is x(x^2-x+1/6)(x-1/2) ?

The solution to x(x^2-x+1/6)(x-1/2) is (x(6x^2-6x+1)(2x-1))/(12)

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simplify x(x^2-x+1/6)(x-1/2)

simplify

x (x^{2} - x + \frac{1}{6}) (x - \frac{1}{2})

\frac{x ( 6 x ^{2} - 6 x + 1 ) ( 2 x - 1 )}{12}

Solution steps

x (x^{2} - x + \frac{1}{6}) (x - \frac{1}{2})

Simplify

x^{2} - x + \frac{1}{6} : \frac{6 x ^{2} - 6 x + 1}{6}

= x \frac{6 x ^{2} - 6 x + 1}{6} (x - \frac{1}{2})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ( 6 x ^{2} - 6 x + 1 ) ( x - \frac{1}{2} )}{6}

Simplify

x (6 x^{2} - 6 x + 1) (x - \frac{1}{2}) : \frac{x ( 6 x ^{2} - 6 x + 1 ) ( x \cdot 2 - 1 )}{2}

= \frac{\frac{x ( 6 x ^{2} - 6 x + 1 ) ( x \cdot 2 - 1 )}{2}}{6}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{x ( 6 x ^{2} - 6 x + 1 ) ( x \cdot 2 - 1 )}{2 \cdot 6}

Multiply the numbers:

2 \cdot 6 = 12

= \frac{x ( 6 x ^{2} - 6 x + 1 ) ( x \cdot 2 - 1 )}{12}

= \frac{x ( 6 x ^{2} - 6 x + 1 ) ( 2 x - 1 )}{12}

(sin (x) + cos (y)) (sin (y) - cos (x))

\frac{e ^{- 4 s} + 2 s}{s ( s - 2 )}

\frac{f ( x ) ( - 7 x + 8 )}{( 2 x - 6 ) ( 7 x + 4 )}

(x - 1) (x - 1 - 3) (x - 1 + 3)

\frac{34 u ( 2 - u )}{1 + 4 u - 2 u ^{2}}

What is x(x^2-x+1/6)(x-1/2) ?
The solution to x(x^2-x+1/6)(x-1/2) is (x(6x^2-6x+1)(2x-1))/(12)