How to solve (a)^(4)-(b)^(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 (a)^(4)-(b)^(4) | Equatix

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Question

$${ a }^{ 4 } - { b }^{ 4 }$$

Factor

$\left(a-b\right)\left(a+b\right)\left(a^{2}+b^{2}\right)$

Solution Steps

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

$$\left(a^{2}-b^{2}\right)\left(a^{2}+b^{2}\right)$$

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

$$\left(a-b\right)\left(a+b\right)$$

Rewrite the complete factored expression.

$$\left(a-b\right)\left(a+b\right)\left(a^{2}+b^{2}\right)$$

Show Solution

Evaluate

$a^{4}-b^{4}$