Let's simplify and analyze these two algebraic expressions step-by-step.
### Expression 1: [tex]\(2 x^2 (x + 2) (x - 2)\)[/tex]
First, let's simplify the given expression:
[tex]\[2 x^2 (x + 2) (x - 2)\][/tex]
Notice that [tex]\((x+2)(x-2)\)[/tex] is a difference of squares. We can simplify this part as follows:
[tex]\[(x+2)(x-2) = x^2 - 4\][/tex]
Substituting this back into the expression, we have:
[tex]\[2 x^2 (x^2 - 4)\][/tex]
This is the simplified form of the first expression. Thus:
[tex]\[2 x^2 (x^2 - 4)\][/tex]
### Expression 2: [tex]\(4 x (x + 2)\)[/tex]
Next, let's simplify the second given expression:
[tex]\[4 x (x + 2)\][/tex]
Distribute [tex]\(4x\)[/tex] across the terms in the parentheses:
[tex]\[4 x \cdot x + 4 x \cdot 2 = 4 x^2 + 8x\][/tex]
So, the simplified form of the second expression is:
[tex]\[4 x^2 + 8x\][/tex]
### Final Results
After simplifying both expressions, we have:
1. [tex]\(2 x^2 (x^2 - 4)\)[/tex]
2. [tex]\(4 x (x + 2)\)[/tex]
Thus, the simplified forms of the given expressions are:
[tex]\[2 x^2 (x^2 - 4) \quad \text{and} \quad 4 x (x + 2)\][/tex]
