How to solve (x)^(4)-(y)^(4)

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)^(4)-(y)^(4) | Equatix

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Question

$${ x }^{ 4 } - { y }^{ 4 }$$

Factor

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

Solution Steps

Rewrite $x^{4}-y^{4}$ as $\left(x^{2}\right)^{2}-\left(y^{2}\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

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

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

$$\left(x-y\right)\left(x+y\right)$$

Rewrite the complete factored expression.

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

Show Solution

Evaluate

$x^{4}-y^{4}$