What is factor p^9+q^9 ?

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

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factor p^9+q^9

factor

p^{9} + q^{9}

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

Solution steps

p^{9} + q^{9}

Apply exponent rules

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

Factor

p^{3} + q^{3} : (p + q) (p^{2} - pq + q^{2})

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

6 x^{2} - 18 x - 18 = 6

1 - \frac{3}{2} x < 4 and \frac{1}{4} x - 2 \leq - 3

\frac{24}{2}

4 (x + 1) + 1 \geq 3 x + 10

3 (z + 4) - 2 (z - 1) = 13

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