What is factor 125a^3b^3-343c^6 ?

The solution to factor 125a^3b^3-343c^6 is (5ab-7c^2)(25a^2b^2+35abc^2+49c^4)

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factor 125a^3b^3-343c^6

factor

125 a^{3} b^{3} - 343 c^{6}

(5 ab - 7 c^{2}) (25 a^{2} b^{2} + 35 ab c^{2} + 49 c^{4})

Solution steps

125 a^{3} b^{3} - 343 c^{6}

Rewrite

125 a^{3} b^{3}

(5 ab)^{3}

Rewrite

343 c^{6}

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

= (5 ab)^{3} - (7 c^{2})^{3}

Apply Difference of Cubes Formula:

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

(5 ab)^{3} - (7 c^{2})^{3} = (5 ab - 7 c^{2}) ((5 ab)^{2} + 5 ab 7 c^{2} + (7 c^{2})^{2})

= (5 ab - 7 c^{2}) ((5 ab)^{2} + 5 ab 7 c^{2} + (7 c^{2})^{2})

Simplify

(5 ab - 7 c^{2}) ((5 ab)^{2} + 5 ab \cdot 7 c^{2} + (7 c^{2})^{2}) : (5 ab - 7 c^{2}) (25 a^{2} b^{2} + 35 ab c^{2} + 49 c^{4})

= (5 ab - 7 c^{2}) (25 a^{2} b^{2} + 35 ab c^{2} + 49 c^{4})

(3 x - 2)^{3} - 3

x^{(e^{2})} + x^{(3 e^{2})}

2 (x + y) - a x - a y

2 x + 4 x e - 2 x^{2}

sin (x^{2} + 3 x)

What is factor 125a^3b^3-343c^6 ?
The solution to factor 125a^3b^3-343c^6 is (5ab-7c^2)(25a^2b^2+35abc^2+49c^4)