Which of the following represents the identity for (a + b + c)²?

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Question: Which of the following represents the identity for (a + b + c)²?

Options:

Correct Answer: a² + b² + c² + 2ab + 2bc + 2ca

Solution:

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

Which of the following represents the identity for (a + b + c)²?

Which of the following represents the identity for (a + b + c)²?

Step 1: Start with the expression (a + b + c)².
Step 2: Recognize that (a + b + c)² means (a + b + c) multiplied by itself.
Step 3: Write it out as (a + b + c) * (a + b + c).
Step 4: Use the distributive property (also known as the FOIL method) to multiply each term in the first group by each term in the second group.
Step 5: Multiply a by each term in (a + b + c): a*a, a*b, a*c.
Step 6: Multiply b by each term in (a + b + c): b*a, b*b, b*c.
Step 7: Multiply c by each term in (a + b + c): c*a, c*b, c*c.
Step 8: Combine all the results from the multiplications: a² + ab + ac + ba + b² + bc + ca + c².
Step 9: Notice that ab and ba are the same, so combine them: a² + b² + c² + 2ab + 2bc + 2ca.
Step 10: The final result is a² + b² + c² + 2ab + 2bc + 2ca, which is the identity for (a + b + c)².

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