Calculate the value of (1 + 3)^5 using the binomial theorem.

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Question: Calculate the value of (1 + 3)^5 using the binomial theorem.

Options:

Correct Answer: 243

Solution:

(1 + 3)^5 = 4^5 = 1024.

Calculate the value of (1 + 3)^5 using the binomial theorem.

Calculate the value of (1 + 3)^5 using the binomial theorem.

Step 1: Identify the expression we need to calculate, which is (1 + 3)^5.
Step 2: Simplify the expression inside the parentheses: 1 + 3 = 4.
Step 3: Now we have 4^5 to calculate.
Step 4: Calculate 4^5. This means multiplying 4 by itself 5 times: 4 * 4 * 4 * 4 * 4.
Step 5: First, calculate 4 * 4 = 16.
Step 6: Next, multiply 16 by 4: 16 * 4 = 64.
Step 7: Then, multiply 64 by 4: 64 * 4 = 256.
Step 8: Finally, multiply 256 by 4: 256 * 4 = 1024.
Step 9: Therefore, the value of (1 + 3)^5 is 1024.

Binomial Theorem – The binomial theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer.
Exponents – Understanding how to calculate powers and the properties of exponents is crucial for simplifying expressions.