Which of the following is the correct identity for (x + y + z)³?

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Question: Which of the following is the correct identity for (x + y + z)³?

Options:

Correct Answer: x³ + y³ + z³ + 3xyz

Solution:

(x + y + z)³ = x³ + y³ + z³ + 3xyz.

Which of the following is the correct identity for (x + y + z)³?

Which of the following is the correct identity for (x + y + z)³?

Step 1: Understand that (x + y + z)³ means you are multiplying (x + y + z) by itself three times.
Step 2: Write it out as (x + y + z) * (x + y + z) * (x + y + z).
Step 3: Use the distributive property to expand the first two (x + y + z) terms.
Step 4: When you expand (x + y + z) * (x + y + z), you get x² + y² + z² + 2xy + 2xz + 2yz.
Step 5: Now, multiply this result by the third (x + y + z) term.
Step 6: Distribute each term from the result of Step 4 with (x + y + z).
Step 7: Combine like terms from the multiplication to simplify the expression.
Step 8: After combining, you will find that the final result is x³ + y³ + z³ + 3xyz.

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