Final answer:
The task is to rearrange the parentheses in the algebraic expression (8x-8-12x+5) to create non-equivalent forms. Multiple arrangements are shown, each changing the groupings and impacts of the operations. The correct simplification of the original expression is also confirmed.
Step-by-step explanation:
The student is asking to change the position of the parentheses in the algebraic expression (8x-8-12x+5) to create a new expression that is not equivalent to the original. To achieve this, we can rearrange the terms and apply the parentheses differently. Here are a few different ways to rearrange the expression:
- (8x-8) - (12x+5): By grouping the first two terms and the last two terms separately, the new expression suggests subtraction.
- (8x) - (8-12x) + 5: In this case, only the first term is isolated in parentheses which may change the sign of the middle term when expanded.
- 8x - (8+12x) + 5: Here, two terms in the middle are grouped together, changing the association of the subtraction.
To eliminate terms wherever possible and simplify the algebra, we combine like terms. For example, in the original expression, 8x and -12x are like terms and can be combined to -4x. Similarly, -8 and 5 are like terms and combine to -3. Therefore, the simplified form of the original expression is -4x - 3. It's important to check that any new expressions created by rearranging the parentheses result in expressions that simplify differently and are not equivalent to -4x - 3 to meet the requirements of the question.
When considering powers within parentheses, as in the example (27x^3)(4x^2) = 2.1 × 10^-33, remember that the power affects everything inside the parentheses.