Question

factor $25k^2 - 9$:
a. $(5k - 3)^2$
b. $(5k + 9)^2$
c. $(4k + 5)(4k - 5)$
d. $(5k + 3)(5k - 3)$

factor $x^4 - 25$:
a. $(x^2)^2 - 5$
b. $(x^2 + 5)(x^2 - 5)$
c. $(x + 5)(x - 5)$
d. $(x^2 + 3)(x^2 - 3)$

Explanation:

Step1: Identify difference of squares

$25k^2 - 9 = (5k)^2 - 3^2$

Step2: Apply difference of squares rule

$a^2 - b^2=(a+b)(a-b)$, so $(5k)^2 - 3^2=(5k+3)(5k-3)$

Step3: Identify difference of squares

$x^4 - 25 = (x^2)^2 - 5^2$

Step4: Apply difference of squares rule

$a^2 - b^2=(a+b)(a-b)$, so $(x^2)^2 - 5^2=(x^2+5)(x^2-5)$

Answer:

1. d. $(5k + 3)(5k - 3)$
2. b. $(x^2 + 5)(x^2 - 5)$