What is factor 1/8-a^3c^{21} ?

The solution to factor 1/8-a^3c^{21} is -(ac^7-1/2)(a^2c^{14}+(ac^7)/2+1/4)

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factor 1/8-a^3c^{21}

factor

\frac{1}{8} - a^{3} c^{21}

- (a c^{7} - \frac{1}{2}) (a^{2} c^{14} + \frac{a c ^{7}}{2} + \frac{1}{4})

Solution steps

\frac{1}{8} - a^{3} c^{21}

Rewrite

a^{3} c^{21}

(a c^{7})^{3}

= \frac{1}{8} - (a c^{7})^{3}

Factor out common term

- 1

= - ((a c^{7})^{3} - \frac{1}{8})

Factor

(a c^{7})^{3} - \frac{1}{8} : (a c^{7} - \frac{1}{2}) ((a c^{7})^{2} + \frac{1}{2} a c^{7} + (\frac{1}{2})^{2})

= - (a c^{7} - \frac{1}{2}) ((a c^{7})^{2} + \frac{1}{2} a c^{7} + (\frac{1}{2})^{2})

Refine

= - (a c^{7} - \frac{1}{2}) ((a c^{7})^{2} + \frac{a c ^{7}}{2} + \frac{1}{4})

Simplify

- (a c^{7} - \frac{1}{2}) ((a c^{7})^{2} + \frac{a c ^{7}}{2} + \frac{1}{4}) : - (a c^{7} - \frac{1}{2}) (a^{2} c^{14} + \frac{a c ^{7}}{2} + \frac{1}{4})

= - (a c^{7} - \frac{1}{2}) (a^{2} c^{14} + \frac{a c ^{7}}{2} + \frac{1}{4})

- 2 (3 x - 4) - x - 3 = 33

n - 3 n = 14 - 4 n

28 + 63

\frac{2 ^{2}}{- 5}

9 a^{2} - 12 ab + 15 a^{3} b^{2} - 24 a b^{3}

What is factor 1/8-a^3c^{21} ?
The solution to factor 1/8-a^3c^{21} is -(ac^7-1/2)(a^2c^{14}+(ac^7)/2+1/4)