What is factor 64a^3b^6c^9-1 ?

The solution to factor 64a^3b^6c^9-1 is (4ab^2c^3-1)(16a^2b^4c^6+4ab^2c^3+1)

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factor 64a^3b^6c^9-1

factor

64 a^{3} b^{6} c^{9} - 1

(4 a b^{2} c^{3} - 1) (16 a^{2} b^{4} c^{6} + 4 a b^{2} c^{3} + 1)

Solution steps

64 a^{3} b^{6} c^{9} - 1

Rewrite

64 a^{3} b^{6} c^{9}

(2^{2} a b^{2} c^{3})^{3}

= (2^{2} a b^{2} c^{3})^{3} - 1

Rewrite

1

1^{3}

= (2^{2} a b^{2} c^{3})^{3} - 1^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(2^{2} a b^{2} c^{3})^{3} - 1^{3} = (2^{2} a b^{2} c^{3} - 1) ((2^{2} a b^{2} c^{3})^{2} + 2^{2} a b^{2} c^{3} + 1)

= (2^{2} a b^{2} c^{3} - 1) ((2^{2} a b^{2} c^{3})^{2} + 2^{2} a b^{2} c^{3} + 1)

Simplify

(2^{2} a b^{2} c^{3} - 1) ((2^{2} a b^{2} c^{3})^{2} + 2^{2} a b^{2} c^{3} + 1) : (4 a b^{2} c^{3} - 1) (16 a^{2} b^{4} c^{6} + 4 a b^{2} c^{3} + 1)

= (4 a b^{2} c^{3} - 1) (16 a^{2} b^{4} c^{6} + 4 a b^{2} c^{3} + 1)

t e^{4 t - s t}

\frac{x ^{2} - 5 x + 6}{x - 2}

(t x) + 2 (t y)

a p + a q + b p + b q

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

What is factor 64a^3b^6c^9-1 ?
The solution to factor 64a^3b^6c^9-1 is (4ab^2c^3-1)(16a^2b^4c^6+4ab^2c^3+1)