Which of the following is the correct identity for (a - b)²?

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Question: Which of the following is the correct identity for (a - b)²?

Options:

Correct Answer: a² - 2ab + b²

Solution:

(a - b)² = a² - 2ab + b² by the expansion of the square of a binomial.

Which of the following is the correct identity for (a - b)²?

Which of the following is the correct identity for (a - b)²?

Step 1: Understand that (a - b)² means (a - b) multiplied by itself.
Step 2: Write it out: (a - b) * (a - b).
Step 3: Use the distributive property (also known as the FOIL method) to multiply: a * (a - b) and -b * (a - b).
Step 4: First, multiply a by a to get a².
Step 5: Next, multiply a by -b to get -ab.
Step 6: Now, multiply -b by a to get -ab again.
Step 7: Finally, multiply -b by -b to get +b².
Step 8: Combine all the results: a² - ab - ab + b².
Step 9: Combine the -ab terms: a² - 2ab + b².
Step 10: Conclude that (a - b)² = a² - 2ab + b².

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