What is factor 125r^6-8b^9 ?

The solution to factor 125r^6-8b^9 is (5r^2-2b^3)(4b^6+25r^4+10r^2b^3)

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factor 125r^6-8b^9

factor

125 r^{6} - 8 b^{9}

(5 r^{2} - 2 b^{3}) (4 b^{6} + 25 r^{4} + 10 r^{2} b^{3})

Solution steps

125 r^{6} - 8 b^{9}

Apply exponent rules

= (5 r^{2})^{3} - (2 b^{3})^{3}

Apply Difference of Cubes Formula:

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

(5 r^{2})^{3} - (2 b^{3})^{3} = (5 r^{2} - 2 b^{3}) ((5 r^{2})^{2} + 5 r^{2} \cdot 2 b^{3} + (2 b^{3})^{2})

= (5 r^{2} - 2 b^{3}) ((5 r^{2})^{2} + 5 r^{2} \cdot 2 b^{3} + (2 b^{3})^{2})

Simplify

(5 r^{2})^{2} + 5 r^{2} \cdot 2 b^{3} + (2 b^{3})^{2} : 25 r^{4} + 10 r^{2} b^{3} + 4 b^{6}

= (5 r^{2} - 2 b^{3}) (25 r^{4} + 10 r^{2} b^{3} + 4 b^{6})

= (5 r^{2} - 2 b^{3}) (4 b^{6} + 25 r^{4} + 10 r^{2} b^{3})

5 (4)^{\frac{1}{4}} + 3 (4)^{\frac{1}{2}} + 5

10 x = 10

4 x^{3} - 36 x^{2} + 80 x

\frac{- 3 x ^{2} y ^{2}}{- x y}

20 + 80

What is factor 125r^6-8b^9 ?
The solution to factor 125r^6-8b^9 is (5r^2-2b^3)(4b^6+25r^4+10r^2b^3)