Question

which expression is equivalent to this polynomial?
$9x^2 + 4$

a. $(3x + 2i)(3x - 2i)$
b. $(3x + 2)(3x - 2)$
c. $(3x + 2i)^2$
d. $(3x + 2)^2$

Explanation:

Step1: Expand Option A (difference of squares)

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

Step2: Calculate each squared term

$(3x)^2 = 9x^2$, $(2i)^2 = 4i^2 = 4(-1) = -4$

Step3: Combine the results

$9x^2 - (-4) = 9x^2 + 4$

Step4: Verify other options (elimination)

Option B: $(3x+2)(3x-2)=9x^2-4$; Option C: $(3x+2i)^2=9x^2+12xi-4$; Option D: $(3x+2)^2=9x^2+12x+4$

Answer:

A. $(3x + 2i)(3x - 2i)$