Question

question 21
factor the following.
$a^4 - 16$
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question 22
factor the following.
$x^2 - 6x + 9$
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Explanation:

Step1: Recognize difference of squares

$a^4 - 16 = (a^2)^2 - 4^2$

Step2: Apply difference of squares formula

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

Step3: Factor remaining difference of squares

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

Step4: Recognize perfect square trinomial

$x^2 - 6x + 9 = x^2 - 2(3)x + 3^2$

Step5: Apply perfect square formula

$x^2 - 2(3)x + 3^2 = (x - 3)^2$

Answer:

1. $(a - 2)(a + 2)(a^2 + 4)$
2. $(x - 3)^2$