Question

example 2 student try
given $f(x) = x^2 - 4$ and $g(x)= x^2 +6$
find $fg$ or $f(x) \cdot g(x)$
$fg =$

Explanation:

Step1: Substitute the given functions

$f(x) \cdot g(x) = (x^2 - 4)(x^2 + 6)$

Step2: Apply distributive property (FOIL)

$= x^2 \cdot x^2 + x^2 \cdot 6 - 4 \cdot x^2 - 4 \cdot 6$

Step3: Simplify each term

$= x^4 + 6x^2 - 4x^2 - 24$

Step4: Combine like terms

$= x^4 + (6x^2 - 4x^2) - 24 = x^4 + 2x^2 - 24$

Answer:

$x^4 + 2x^2 - 24$