Which of the following is the correct expansion of (x - y)³?

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Question: Which of the following is the correct expansion of (x - y)³?

Options:

Correct Answer: x³ - 3x²y + 3xy² - y³

Solution:

(x - y)³ = x³ - 3x²y + 3xy² - y³ by the binomial theorem.

Which of the following is the correct expansion of (x - y)³?

Which of the following is the correct expansion of (x - y)³?

Step 1: Understand that (x - y)³ means (x - y) multiplied by itself three times: (x - y) * (x - y) * (x - y).
Step 2: First, calculate (x - y) * (x - y). This gives you x² - 2xy + y².
Step 3: Now, take the result from Step 2, which is (x² - 2xy + y²), and multiply it by (x - y) again.
Step 4: Distribute (x - y) across (x² - 2xy + y²): First, multiply x by each term: x * x² = x³, x * (-2xy) = -2x²y, and x * y² = xy².
Step 5: Now, multiply -y by each term: -y * x² = -yx², -y * (-2xy) = 2y²x, and -y * y² = -y³.
Step 6: Combine all the results from Steps 4 and 5: x³ - 2x²y + xy² - yx² + 2y²x - y³.
Step 7: Rearrange and combine like terms: x³ - 3x²y + 3xy² - y³.

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