The Correct Answer and Explanation is:
The correct answer is 2x² + 15x – 24.
To simplify the algebraic expression 2x(x + 6) + 3(x – 8), you must follow a systematic process involving the distributive property and combining like terms. This ensures that the expression is reduced to its simplest form.
First, we apply the distributive property to each part of the expression. The distributive property states that a term multiplied by a sum or difference in parentheses is equal to the sum or difference of that term multiplied by each term inside the parentheses.
Let’s start with the first term, 2x(x + 6). We need to multiply 2x by both terms inside the parentheses.
- Multiply 2x by x: 2x * x = 2x².
- Multiply 2x by 6: 2x * 6 = 12x.
Combining these results, the expansion of 2x(x + 6) is 2x² + 12x.
Next, we apply the same principle to the second term, 3(x – 8). We multiply 3 by both terms inside its parentheses.
- Multiply 3 by x: 3 * x = 3x.
- Multiply 3 by -8: 3 * -8 = -24.
So, the expansion of 3(x – 8) is 3x – 24.
Now, we substitute these expanded parts back into the original expression. The problem 2x(x + 6) + 3(x – 8) becomes (2x² + 12x) + (3x – 24).
The final step is to combine the like terms. Like terms are terms that contain the same variable raised to the same power.
- The x² term is 2x², and there are no other x² terms to combine it with.
- The x terms are 12x and 3x. We add their coefficients: 12 + 3 = 15. This gives us 15x.
- The constant term is -24, which has no other constant terms to combine with.
By putting all the simplified parts together, we get the final answer: 2x² + 15x – 24.
