What is factor 125x^{3m}-216y^{9m} ?

The solution to factor 125x^{3m}-216y^{9m} is (5x^m-6y^{3m})(25x^{2m}+30x^my^{3m}+36y^{6m})

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factor 125x^{3m}-216y^{9m}

factor

125 x^{3 m} - 216 y^{9 m}

(5 x^{m} - 6 y^{3 m}) (25 x^{2 m} + 30 x^{m} y^{3 m} + 36 y^{6 m})

Solution steps

125 x^{3 m} - 216 y^{9 m}

Rewrite

125 x^{3 m}

(5 x^{1 m})^{3}

Rewrite

216 y^{9 m}

(6 y^{3 m})^{3}

= (5 x^{1 \cdot m})^{3} - (6 y^{3 m})^{3}

Apply Difference of Cubes Formula:

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

(5 x^{1 m})^{3} - (6 y^{3 m})^{3} = (5 x^{1 m} - 6 y^{3 m}) ((5 x^{1 m})^{2} + 6 y^{3 m} 5 x^{1 m} + (6 y^{3 m})^{2})

= (5 x^{1 m} - 6 y^{3 m}) ((6 y^{3 m})^{2} + 6 y^{3 m} 5 x^{1 m} + (5 x^{1 m})^{2})

Simplify

(5 x^{1 \cdot m} - 6 y^{3 m}) ((5 x^{1 \cdot m})^{2} + 6 y^{3 m} \cdot 5 x^{1 \cdot m} + (6 y^{3 m})^{2}) : (5 x^{m} - 6 y^{3 m}) (25 x^{2 m} + 30 x^{m} y^{3 m} + 36 y^{6 m})

= (5 x^{m} - 6 y^{3 m}) (25 x^{2 m} + 30 x^{m} y^{3 m} + 36 y^{6 m})

r (22 π)

ma + mb - na - nb

(a + b - 1) (a^{2} + 1) - a^{2} 1

16 x^{2} + (- 96 x)

x^{2} + 9 + 16

What is factor 125x^{3m}-216y^{9m} ?
The solution to factor 125x^{3m}-216y^{9m} is (5x^m-6y^{3m})(25x^{2m}+30x^my^{3m}+36y^{6m})