Question

question 23
factor the following.
$x^2 - 12x + 36$
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question 24
factor the following.
$y^3 - 64$
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Explanation:

Step1: Recognize perfect square trinomial

$x^2 - 12x + 36$ matches $a^2-2ab+b^2$, where $a=x$, $b=6$

Step2: Apply perfect square formula

$a^2-2ab+b^2=(a-b)^2$, so $x^2-12x+36=(x-6)^2$

Step3: Recognize difference of cubes

$y^3 - 64 = y^3 - 4^3$, matches $a^3-b^3$

Step4: Apply difference of cubes formula

$a^3-b^3=(a-b)(a^2+ab+b^2)$, so $y^3-4^3=(y-4)(y^2+4y+16)$

Answer:

1. $(x-6)^2$
2. $(y-4)(y^2+4y+16)$