What is factor p^6q^9+r^3 ?

The solution to factor p^6q^9+r^3 is (p^2q^3+r)(p^4q^6-p^2q^3r+r^2)

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factor p^6q^9+r^3

factor

p^{6} q^{9} + r^{3}

(p^{2} q^{3} + r) (p^{4} q^{6} - p^{2} q^{3} r + r^{2})

Solution steps

p^{6} q^{9} + r^{3}

Rewrite

p^{6} q^{9}

(p^{2} q^{3})^{3}

= (p^{2} q^{3})^{3} + r^{3}

Apply Sum of Cubes Formula:

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

(p^{2} q^{3})^{3} + r^{3} = (p^{2} q^{3} + r) ((p^{2} q^{3})^{2} - p^{2} q^{3} r + r^{2})

= (r + p^{2} q^{3}) ((p^{2} q^{3})^{2} - r p^{2} q^{3} + r^{2})

Simplify

(p^{2} q^{3} + r) ((p^{2} q^{3})^{2} - p^{2} q^{3} r + r^{2}) : (p^{2} q^{3} + r) (p^{4} q^{6} - p^{2} q^{3} r + r^{2})

= (p^{2} q^{3} + r) (p^{4} q^{6} - p^{2} q^{3} r + r^{2})

4 r^{2} - π r^{2}

3 (x + y)^{2} - 4 (x + y) - 4

5 (x + y)^{2} - 17 (x + y) + 6

\frac{63}{1 + 8 e ^{- 315 (5)}}

\frac{d}{d t} ((x) (t^{2}))

What is factor p^6q^9+r^3 ?
The solution to factor p^6q^9+r^3 is (p^2q^3+r)(p^4q^6-p^2q^3r+r^2)