If -1 < X < Y < 0, which of the following expressions are listed in order from least to greatest?

Explanation

Given -1 < X < Y < 0, both X and Y are negative.

Let's analyze the expressions:

xy²: Since y² is positive (because squaring a number makes it positive), and x is negative, xy² is negative.

x²y: Since x² is positive, and y is negative, x²y is negative.

xy: Since both x and y are negative, xy is positive.

Comparing the signs:

xy is positive.

Both xy² and x²y are negative.

Since xy is positive and the others are negative, xy must be the greatest.

Now, comparing xy² and x²y:

Let's consider the magnitude:

|x| > |y| (since X < Y < 0)

xy² = x * y² (x is more negative, y² is positive)

x²y = x² * y (x² is positive, y is negative)

Given |x| > |y|, x² > y² (since both are positive after squaring)

x²|y| > |x|y² (since |y| < |x| and both x² and y² are positive)

x²y < xy² (both are negative, but x²y is more negative)

So, the order from least to greatest is:

x²y, xy², xy

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