What is factor 1000a^6-343b^3c^6 ?

The solution to factor 1000a^6-343b^3c^6 is (10a^2-7bc^2)(100a^4+70a^2bc^2+49b^2c^4)

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factor 1000a^6-343b^3c^6

factor

1000 a^{6} - 343 b^{3} c^{6}

(10 a^{2} - 7 b c^{2}) (100 a^{4} + 70 a^{2} b c^{2} + 49 b^{2} c^{4})

Solution steps

1000 a^{6} - 343 b^{3} c^{6}

Rewrite

1000 a^{6}

(10 a^{2})^{3}

Rewrite

343 b^{3} c^{6}

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

= (10 a^{2})^{3} - (7 b c^{2})^{3}

Apply Difference of Cubes Formula:

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

(10 a^{2})^{3} - (7 b c^{2})^{3} = (10 a^{2} - 7 b c^{2}) ((10 a^{2})^{2} + 10 a^{2} 7 b c^{2} + (7 b c^{2})^{2})

= (10 a^{2} - 7 b c^{2}) ((10 a^{2})^{2} + 10 a^{2} 7 b c^{2} + (7 b c^{2})^{2})

Simplify

(10 a^{2} - 7 b c^{2}) ((10 a^{2})^{2} + 10 a^{2} \cdot 7 b c^{2} + (7 b c^{2})^{2}) : (10 a^{2} - 7 b c^{2}) (100 a^{4} + 70 a^{2} b c^{2} + 49 b^{2} c^{4})

= (10 a^{2} - 7 b c^{2}) (100 a^{4} + 70 a^{2} b c^{2} + 49 b^{2} c^{4})

(x - 2) + (x - 2)

3 (7 x c - 8 y d + 56 x d - yc)

am - bm + an - bm

x^{2} - 6 + 8

x^{2} - 6 + 9

What is factor 1000a^6-343b^3c^6 ?
The solution to factor 1000a^6-343b^3c^6 is (10a^2-7bc^2)(100a^4+70a^2bc^2+49b^2c^4)