Question

what is the simplest form of this binomial expression?
a⁴ − b⁴
select the correct answer.
○ (a − b) (a − b) (a² + b²)
○ (a + b) (a − b) (a² + b²)
○ (a + b) (a + b) (a² + b²)
○ (a + b) (a − b) (a² − b²)

Explanation:

Step1: Recognize difference of squares

$a^4 - b^4 = (a^2)^2 - (b^2)^2$

Step2: Apply difference of squares formula

$(a^2)^2 - (b^2)^2 = (a^2 - b^2)(a^2 + b^2)$

Step3: Factor $a^2 - b^2$ further

$a^2 - b^2 = (a + b)(a - b)$

Step4: Combine all factors

$(a + b)(a - b)(a^2 + b^2)$

Answer:

$(a + b)(a - b)(a^2 + b^2)$