What is factor 8a^3-b^6c^3 ?

The solution to factor 8a^3-b^6c^3 is (2a-b^2c)(4a^2+2ab^2c+b^4c^2)

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factor 8a^3-b^6c^3

factor

8 a^{3} - b^{6} c^{3}

(2 a - b^{2} c) (4 a^{2} + 2 a b^{2} c + b^{4} c^{2})

Solution steps

8 a^{3} - b^{6} c^{3}

Rewrite

8 a^{3}

(2 a)^{3}

Rewrite

b^{6} c^{3}

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

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(2 a - b^{2} c) ((2 a)^{2} + 2 a b^{2} c + (b^{2} c)^{2}) : (2 a - b^{2} c) (4 a^{2} + 2 a b^{2} c + b^{4} c^{2})

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

9 x^{12} + 4 x^{6}

x^{2} + x^{2} - b x - b z

(x y^{2}) + 1 - x^{2} - y^{2}

4^{x} + 3 (2^{x}) - 18

100000 e^{(2199)}

What is factor 8a^3-b^6c^3 ?
The solution to factor 8a^3-b^6c^3 is (2a-b^2c)(4a^2+2ab^2c+b^4c^2)