Question

Form first to last order.The steps to prove that expression a is equivalent to expression b (x+4)(×-2)
X^2+2x-8

Answer 1

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 \( x^2 + 2x - 8 \).