Which of the following is true for the identity (x + y)²?

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Question: Which of the following is true for the identity (x + y)²?

Options:

Correct Answer: x² + 2xy + y²

Solution:

(x + y)² = x² + 2xy + y².

Which of the following is true for the identity (x + y)²?

Which of the following is true for the identity (x + y)²?

Step 1: Start with the expression (x + y)².
Step 2: Understand that (x + y)² means (x + y) multiplied by itself: (x + y) * (x + y).
Step 3: Use the distributive property (also known as the FOIL method for binomials) to multiply the two expressions.
Step 4: Multiply the first terms: x * x = x².
Step 5: Multiply the outer terms: x * y = xy.
Step 6: Multiply the inner terms: y * x = xy.
Step 7: Multiply the last terms: y * y = y².
Step 8: Combine all the results: x² + xy + xy + y².
Step 9: Simplify by combining like terms (the two xy terms): x² + 2xy + y².
Step 10: Conclude that (x + y)² = x² + 2xy + y² is true.

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