What is (1/3+x/2)(1/9-(x^2)/4)(1/3-x/2) ?

The solution to (1/3+x/2)(1/9-(x^2)/4)(1/3-x/2) is ((2+3x)(4-9x^2)(2-3x))/(1296)

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simplify (1/3+x/2)(1/9-(x^2)/4)(1/3-x/2)

simplify

(\frac{1}{3} + \frac{x}{2}) (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2})

\frac{( 2 + 3 x ) ( 4 - 9 x ^{2} ) ( 2 - 3 x )}{1296}

Solution steps

(\frac{1}{3} + \frac{x}{2}) (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2})

Simplify

\frac{1}{3} + \frac{x}{2} : \frac{2 + 3 x}{6}

= \frac{2 + 3 x}{6} (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2})

Apply the fraction rule:

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

= \frac{( 2 + 3 x ) ( \frac{1}{9} - \frac{x ^{2}}{4} ) ( \frac{1}{3} - \frac{x}{2} )}{6}

Simplify

(2 + 3 x) (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2}) : \frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{216}

= \frac{\frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{216}}{6}

Apply the fraction rule:

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

= \frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{216 \cdot 6}

Multiply the numbers:

216 \cdot 6 = 1296

= \frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{1296}

= \frac{( 2 + 3 x ) ( 4 - 9 x ^{2} ) ( 2 - 3 x )}{1296}

(8 x^{3} - \frac{12}{x ^{3}}) (4 x^{2} - \frac{6}{x ^{4}})

(4 x - \frac{1}{2} y)^{4}

x (\frac{3 x}{4} + \frac{10 - 3 x}{2})

3 (2 x^{3} + 1) (x^{4} + 2 x)^{\frac{1}{2}}

What is (1/3+x/2)(1/9-(x^2)/4)(1/3-x/2) ?
The solution to (1/3+x/2)(1/9-(x^2)/4)(1/3-x/2) is ((2+3x)(4-9x^2)(2-3x))/(1296)