Find the value of (1 + x)^6 when x = 2.

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Question: Find the value of (1 + x)^6 when x = 2.

Options:

Correct Answer: 256

Solution:

Using the binomial theorem, (1 + 2)^6 = 3^6 = 729.

Find the value of (1 + x)^6 when x = 2.

Find the value of (1 + x)^6 when x = 2.

Step 1: Identify the expression we need to evaluate, which is (1 + x)^6.
Step 2: Substitute the value of x into the expression. Here, x = 2, so we have (1 + 2)^6.
Step 3: Simplify the expression inside the parentheses. 1 + 2 equals 3, so we now have (3)^6.
Step 4: Calculate 3 raised to the power of 6. This means multiplying 3 by itself 6 times: 3 * 3 * 3 * 3 * 3 * 3.
Step 5: Perform the multiplication step by step: 3 * 3 = 9, then 9 * 3 = 27, then 27 * 3 = 81, then 81 * 3 = 243, and finally 243 * 3 = 729.
Step 6: The final result is 729.

Binomial Theorem – The binomial theorem provides a formula for expanding expressions of the form (a + b)^n.
Substitution – The process of replacing a variable with a specific value in an expression.
Exponentiation – The operation of raising a number to a power, which involves multiplying the number by itself a certain number of times.