What is factor 125a^6b^3-64c^3 ?

The solution to factor 125a^6b^3-64c^3 is (5a^2b-4c)(25a^4b^2+20a^2bc+16c^2)

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factor 125a^6b^3-64c^3

factor

125 a^{6} b^{3} - 64 c^{3}

(5 a^{2} b - 4 c) (25 a^{4} b^{2} + 20 a^{2} b c + 16 c^{2})

Solution steps

125 a^{6} b^{3} - 64 c^{3}

Rewrite

125 a^{6} b^{3}

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

Rewrite

64 c^{3}

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

= (5 a^{2} b)^{3} - (2^{2} c)^{3}

Apply Difference of Cubes Formula:

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

(5 a^{2} b)^{3} - (2^{2} c)^{3} = (5 a^{2} b - 2^{2} c) ((5 a^{2} b)^{2} + 2^{2} c 5 a^{2} b + (2^{2} c)^{2})

= (5 a^{2} b - 2^{2} c) ((2^{2} c)^{2} + 2^{2} c 5 a^{2} b + (5 a^{2} b)^{2})

Simplify

(5 a^{2} b - 2^{2} c) ((5 a^{2} b)^{2} + 2^{2} c \cdot 5 a^{2} b + (2^{2} c)^{2}) : (5 a^{2} b - 4 c) (25 a^{4} b^{2} + 20 a^{2} b c + 16 c^{2})

= (5 a^{2} b - 4 c) (25 a^{4} b^{2} + 20 a^{2} b c + 16 c^{2})

H Cl O^{3} + S r (O H) 2

\frac{x ^{4} - 1}{x ^{3} - 1}

[0.5]

a^{3} + (a + 1)^{3}

\frac{d}{d x} ((f (x)) (x^{3}))

What is factor 125a^6b^3-64c^3 ?
The solution to factor 125a^6b^3-64c^3 is (5a^2b-4c)(25a^4b^2+20a^2bc+16c^2)