Which of the following expressions is equivalent to (x + 2)(x - 3)?

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Question: Which of the following expressions is equivalent to (x + 2)(x - 3)?

Options:

Correct Answer: x^2 - x - 6

Solution:

Expanding (x + 2)(x - 3) gives x^2 - 3x + 2x - 6 = x^2 - x - 6.

Which of the following expressions is equivalent to (x + 2)(x - 3)?

Which of the following expressions is equivalent to (x + 2)(x - 3)?

Step 1: Start with the expression (x + 2)(x - 3).
Step 2: Use the distributive property (also known as the FOIL method) to multiply the two binomials.
Step 3: Multiply the first terms: x * x = x^2.
Step 4: Multiply the outer terms: x * -3 = -3x.
Step 5: Multiply the inner terms: 2 * x = 2x.
Step 6: Multiply the last terms: 2 * -3 = -6.
Step 7: Combine all the results from steps 3, 4, 5, and 6: x^2 - 3x + 2x - 6.
Step 8: Combine like terms: -3x + 2x = -x.
Step 9: Write the final expression: x^2 - x - 6.

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