Question

|4x^2-9y|

Answer 1

[AI-generated answer — Bot GPT 3.5]

The expression is the absolute value of the difference between 4x^2 and 9y.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression |4x^2-9y|, we need to consider two cases: when the expression inside the absolute value is positive, and when it is negative.

Case 1: When 4x^2-9y is positive or zero
In this case, we can simply remove the absolute value without changing the expression:
|4x^2-9y| = 4x^2-9y

Case 2: When 4x^2-9y is negative
When the expression inside the absolute value is negative, we need to change its sign and remove the absolute value bars:
|4x^2-9y| = -(4x^2-9y)

Therefore, the simplified expression for |4x^2-9y| is:
- (4x^2-9y) when 4x^2-9y is negative,
or
4x^2-9y when 4x^2-9y is positive or zero.

Answer 3

[AI-generated answer — Explain Bot]

To simplify the expression |4x^2 - 9y|, you need to remove the absolute value brackets. The expression inside the absolute value brackets, 4x^2 - 9y, can be both positive or negative, so we need to consider both cases.

Case 1: (4x^2 - 9y) ≥ 0
In this case, the expression inside the absolute value brackets is either positive or zero. Therefore, we can write |4x^2 - 9y| as (4x^2 - 9y). No further simplification is required.

Case 2: (4x^2 - 9y) < 0
In this case, the expression inside the absolute value brackets is negative. When we take the absolute value of a negative number, it becomes positive. So, in this case, |4x^2 - 9y| can be written as -(4x^2 - 9y). To simplify further, we can distribute the negative sign: -4x^2 + 9y.

Therefore, the simplified expression for |4x^2 - 9y| is (4x^2 - 9y) if (4x^2 - 9y) ≥ 0, and -4x^2 + 9y if (4x^2 - 9y) < 0.