To prove that the expression \( (x+4)(x-2) \) is equivalent to \( x^2 + 2x - 8 \), we can follow these steps:
Step 1: Expand the Expression
We will expand the expression \( (x+4)(x-2) \).
\[ (x + 4)(x - 2) = x^2 - 2x + 4x - 8 \]
Step 2: Combine Like Terms
Combine the like terms in the expanded expression.
\[ x^2 - 2x + 4x - 8 = x^2 + 2x - 8 \]
Step 3: Compare Expressions
Now, we compare the result obtained from the expansion, \( x^2 + 2x - 8 \), with the given expression.
\[ x^2 + 2x - 8 \text{ (from expansion)} \quad \text{and} \quad x^2 + 2x - 8 \text{ (given)} \]
Step 4: Conclude the Proof
Since both expressions are equivalent after expanding and simplifying, we conclude that:
\[ (x + 4)(x - 2) = x^2 + 2x - 8 \]
Final Statement
Therefore, we have proven that the expression \( (x + 4)(x - 2) \) is equivalent to \( x^2 + 2x - 8 \).