Question

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

factor $n^4 - 4$:
a. $(n^2 + 4)^2$
b. $(n^2 + 2)(n^2 - 2)$
c. $(3n^2 + 5)(3n^2 - 5)$
d. not factorable

Explanation:

Step1: Identify difference of squares

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

Step2: Apply difference of squares formula

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

Step3: Identify difference of squares

$n^4 - 4 = (n^2)^2 - 2^2$

Step4: Apply difference of squares formula

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

Answer:

1. c. $(3x + 5)(3x - 5)$
2. b. $(n^2 + 2)(n^2 - 2)$