Which of the following expressions represents the polynomial obtained by multipl

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Question: Which of the following expressions represents the polynomial obtained by multiplying (x + 1) and (x - 1)?

Options:

Correct Answer: x^2 - 1

Solution:

The product (x + 1)(x - 1) is a difference of squares, resulting in x^2 - 1.

Which of the following expressions represents the polynomial obtained by multiplying (x + 1) and (x - 1)?

Which of the following expressions represents the polynomial obtained by multiplying (x + 1) and (x - 1)?

Step 1: Identify the two expressions you need to multiply: (x + 1) and (x - 1).
Step 2: Recognize that this multiplication is a special case called the 'difference of squares'.
Step 3: Recall the formula for the difference of squares: (a + b)(a - b) = a^2 - b^2.
Step 4: In our case, a is x and b is 1. So, we can apply the formula.
Step 5: Substitute a and b into the formula: (x + 1)(x - 1) = x^2 - 1^2.
Step 6: Calculate 1^2, which is 1.
Step 7: Write the final result: x^2 - 1.

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