What is factor r^9-1000s^{12} ?

The solution to factor r^9-1000s^{12} is (r^3-10s^4)(r^6+10r^3s^4+100s^8)

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factor r^9-1000s^{12}

factor

r^{9} - 1000 s^{12}

(r^{3} - 10 s^{4}) (r^{6} + 10 r^{3} s^{4} + 100 s^{8})

Solution steps

r^{9} - 1000 s^{12}

Apply exponent rules

= (r^{3})^{3} - (10 s^{4})^{3}

Apply Difference of Cubes Formula:

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

(r^{3})^{3} - (10 s^{4})^{3} = (r^{3} - 10 s^{4}) ((r^{3})^{2} + r^{3} \cdot 10 s^{4} + (10 s^{4})^{2})

= (r^{3} - 10 s^{4}) ((r^{3})^{2} + r^{3} \cdot 10 s^{4} + (10 s^{4})^{2})

Simplify

(r^{3})^{2} + r^{3} \cdot 10 s^{4} + (10 s^{4})^{2} : r^{6} + 10 r^{3} s^{4} + 100 s^{8}

= (r^{3} - 10 s^{4}) (r^{6} + 10 r^{3} s^{4} + 100 s^{8})

- 10 \cdot 5

- (- 1)^{- 1}

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

\frac{1}{20}

\frac{- 10}{10}

What is factor r^9-1000s^{12} ?
The solution to factor r^9-1000s^{12} is (r^3-10s^4)(r^6+10r^3s^4+100s^8)