What is factor 8a^6b^3+125c^3 ?

The solution to factor 8a^6b^3+125c^3 is (2a^2b+5c)(4a^4b^2-10a^2bc+25c^2)

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factor 8a^6b^3+125c^3

factor

8 a^{6} b^{3} + 125 c^{3}

(2 a^{2} b + 5 c) (4 a^{4} b^{2} - 10 a^{2} b c + 25 c^{2})

Solution steps

8 a^{6} b^{3} + 125 c^{3}

Rewrite

8 a^{6} b^{3}

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

Rewrite

125 c^{3}

(5 c)^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(2 a^{2} b + 5 c) ((2 a^{2} b)^{2} - 2 a^{2} b \cdot 5 c + (5 c)^{2}) : (2 a^{2} b + 5 c) (4 a^{4} b^{2} - 10 a^{2} b c + 25 c^{2})

= (2 a^{2} b + 5 c) (4 a^{4} b^{2} - 10 a^{2} b c + 25 c^{2})

(x + 5) (x + 5)

a m^{2} + b m^{2} + a n^{2} + b n^{2}

\frac{x - 1}{x - 1}

4^{2} - 9

- cos (9 α + 6 θ) sin (9 α + 6 θ)

What is factor 8a^6b^3+125c^3 ?
The solution to factor 8a^6b^3+125c^3 is (2a^2b+5c)(4a^4b^2-10a^2bc+25c^2)