What is factor 1000y^9-m^{15} ?

The solution to factor 1000y^9-m^{15} is (10y^3-m^5)(100y^6+10y^3m^5+m^{10})

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factor 1000y^9-m^{15}

factor

1000 y^{9} - m^{15}

(10 y^{3} - m^{5}) (100 y^{6} + 10 y^{3} m^{5} + m^{10})

Solution steps

1000 y^{9} - m^{15}

Apply exponent rules

= (10 y^{3})^{3} - (m^{5})^{3}

Apply Difference of Cubes Formula:

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

(10 y^{3})^{3} - (m^{5})^{3} = (10 y^{3} - m^{5}) ((10 y^{3})^{2} + 10 y^{3} m^{5} + (m^{5})^{2})

= (10 y^{3} - m^{5}) ((10 y^{3})^{2} + 10 y^{3} m^{5} + (m^{5})^{2})

Simplify

(10 y^{3})^{2} + 10 y^{3} m^{5} + (m^{5})^{2} : 100 y^{6} + 10 y^{3} m^{5} + m^{10}

= (10 y^{3} - m^{5}) (100 y^{6} + 10 y^{3} m^{5} + m^{10})

25 n^{3} + 15 n^{2} + 20 n + 12

x^{\frac{5}{2}} - 36 x^{\frac{1}{2}}

- 5 x > 20

- 2 ∣ 7 d ∣ + 9 \geq - 7

3 (3 x - 8) = 4 x + 6

What is factor 1000y^9-m^{15} ?
The solution to factor 1000y^9-m^{15} is (10y^3-m^5)(100y^6+10y^3m^5+m^{10})