How to solve x ^ 9 + y ^ 9

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve x ^ 9 + y ^ 9 | Equatix

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Question

$$x^{9}+y^{9}$$

Factor

$\left(x+y\right)\left(x^{2}-xy+y^{2}\right)\left(x^{6}-x^{3}y^{3}+y^{6}\right)$

Solution Steps

Rewrite $x^{9}+y^{9}$ as $\left(x^{3}\right)^{3}+\left(y^{3}\right)^{3}$. The sum of cubes can be factored using the rule: $a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right)$.

$$\left(x^{3}+y^{3}\right)\left(x^{6}-x^{3}y^{3}+y^{6}\right)$$

Consider $x^{3}+y^{3}$. The sum of cubes can be factored using the rule: $a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right)$.

$$\left(x+y\right)\left(x^{2}-xy+y^{2}\right)$$

Rewrite the complete factored expression.

$$\left(x+y\right)\left(x^{2}-xy+y^{2}\right)\left(x^{6}-x^{3}y^{3}+y^{6}\right)$$

Show Solution

Evaluate

$x^{9}+y^{9}$