Question: Which of the following is the correct identity for (x + y)³?
Options:
x³ + y³ + 3xy(x + y)
x³ + y³ - 3xy(x + y)
x³ + y³ + 3xy²
x³ - y³
Correct Answer: x³ + y³ + 3xy(x + y)
Solution:
(x + y)³ = x³ + y³ + 3xy(x + y) by the binomial expansion.
Which of the following is the correct identity for (x + y)³?
Practice Questions
Q1
Which of the following is the correct identity for (x + y)³?
x³ + y³ + 3xy(x + y)
x³ + y³ - 3xy(x + y)
x³ + y³ + 3xy²
x³ - y³
Questions & Step-by-Step Solutions
Which of the following is the correct identity for (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: Use the binomial expansion formula, which helps us expand expressions like (a + b)ⁿ. For (x + y)³, we can use the formula: (a + b)³ = a³ + b³ + 3ab(a + b).
Step 3: In our case, let a = x and b = y. So, we replace a and b in the formula: (x + y)³ = x³ + y³ + 3xy(x + y).
Step 4: Write down the final expanded form: (x + y)³ = x³ + y³ + 3xy(x + y).
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