What is factor a^3b^6c^9+1000 ?

The solution to factor a^3b^6c^9+1000 is (ab^2c^3+10)(a^2b^4c^6-10ab^2c^3+100)

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factor a^3b^6c^9+1000

factor

a^{3} b^{6} c^{9} + 1000

(a b^{2} c^{3} + 10) (a^{2} b^{4} c^{6} - 10 a b^{2} c^{3} + 100)

Solution steps

a^{3} b^{6} c^{9} + 1000

Rewrite

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

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

= (a b^{2} c^{3})^{3} + 1000

Rewrite

1000

1 0^{3}

= (a b^{2} c^{3})^{3} + 1 0^{3}

Apply Sum of Cubes Formula:

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

(a b^{2} c^{3})^{3} + 1 0^{3} = (a b^{2} c^{3} + 10) ((a b^{2} c^{3})^{2} - 10 a b^{2} c^{3} + 1 0^{2})

= (a b^{2} c^{3} + 10) ((a b^{2} c^{3})^{2} - 10 a b^{2} c^{3} + 1 0^{2})

Refine

= (a b^{2} c^{3} + 10) ((a b^{2} c^{3})^{2} - 10 a b^{2} c^{3} + 100)

Simplify

(a b^{2} c^{3} + 10) ((a b^{2} c^{3})^{2} - 10 a b^{2} c^{3} + 100) : (a b^{2} c^{3} + 10) (a^{2} b^{4} c^{6} - 10 a b^{2} c^{3} + 100)

= (a b^{2} c^{3} + 10) (a^{2} b^{4} c^{6} - 10 a b^{2} c^{3} + 100)

- x + 6 \cdot 2 + x - 2

\frac{x - 4}{x ^{2} - x - 12}

13.33

ab c + ab + a c + b c + a + b + c + 1

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

What is factor a^3b^6c^9+1000 ?
The solution to factor a^3b^6c^9+1000 is (ab^2c^3+10)(a^2b^4c^6-10ab^2c^3+100)