Question

These algebraic expressions are not equivalent. Explain why they are not equivalent.

x^2 - 1/2 + 8x - x^2 - 6x = 2x^2 - 2x

Answer 1

The algebraic expressions x^2 - 1/2 + 8x - x^2 - 6x and 2x^2 - 2x are not equivalent because they have different terms that cannot be combined.

Step-by-step explanation:

The algebraic expressions x^2 - 1/2 + 8x - x^2 - 6x and 2x^2 - 2x are not equivalent. To understand why, we need to simplify both expressions. Starting with the first expression:

x^2 - 1/2 + 8x - x^2 - 6x

Simplifying, we can combine like terms, which are terms with the same variables and exponents:

8x - 6x = 2x

The simplified expression becomes:

2x - 1/2

Now, let's simplify the second expression:

2x^2 - 2x

Here, we cannot combine any like terms because the terms have different exponents.

Therefore, the expressions are not equivalent.