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

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

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

factor

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

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

Solution steps

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

Rewrite

27 a^{21}

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

Rewrite

1000 b^{3} z^{12}

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

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

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

Simplify

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

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

(x^{2}) - (y^{2})

5^{n + 3} + 5^{n}

(x + i y) - 1 + i

f (x) = 7 x - 2

l [e^{- 2 x}]

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