What is factor 27a^{21}-1000b^3c^{12} ?

The solution to factor 27a^{21}-1000b^3c^{12} is (3a^7-10bc^4)(9a^{14}+30a^7bc^4+100b^2c^8)

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factor 27a^{21}-1000b^3c^{12}

factor

27 a^{21} - 1000 b^{3} c^{12}

(3 a^{7} - 10 b c^{4}) (9 a^{14} + 30 a^{7} b c^{4} + 100 b^{2} c^{8})

Solution steps

27 a^{21} - 1000 b^{3} c^{12}

Rewrite

27 a^{21}

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

Rewrite

1000 b^{3} c^{12}

(10 b c^{4})^{3}

= (3 a^{7})^{3} - (10 b c^{4})^{3}

Apply Difference of Cubes Formula:

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

(3 a^{7})^{3} - (10 b c^{4})^{3} = (3 a^{7} - 10 b c^{4}) ((3 a^{7})^{2} + 10 b c^{4} 3 a^{7} + (10 b c^{4})^{2})

= (3 a^{7} - 10 b c^{4}) ((10 b c^{4})^{2} + 10 b c^{4} 3 a^{7} + (3 a^{7})^{2})

Simplify

(3 a^{7} - 10 b c^{4}) ((3 a^{7})^{2} + 10 b c^{4} \cdot 3 a^{7} + (10 b c^{4})^{2}) : (3 a^{7} - 10 b c^{4}) (9 a^{14} + 30 a^{7} b c^{4} + 100 b^{2} c^{8})

= (3 a^{7} - 10 b c^{4}) (9 a^{14} + 30 a^{7} b c^{4} + 100 b^{2} c^{8})

16 - 4

(x + y + 2) 4 x + (x + y + 2) 6 x

(5 x + 3)^{2} + 6 (5 x + 3) + 9

(4 x y^{2}) - 3

a x + a y + 4 x + 4 y

What is factor 27a^{21}-1000b^3c^{12} ?
The solution to factor 27a^{21}-1000b^3c^{12} is (3a^7-10bc^4)(9a^{14}+30a^7bc^4+100b^2c^8)