2. Expand and simplify the following product, using the distributive property:
(𝑥 − 3)(𝑥 + 2).
Applying the distributive property, we get:
𝑥(𝑥 + 2) - 3(𝑥 + 2)
Expanding each term, we get:
𝑥² + 2𝑥 - 3𝑥 - 6
Combining like terms, we get:
𝑥² - 𝑥 - 6
To expand and simplify the product (𝑥 − 3)(𝑥 + 2) using the distributive property, we multiply each term of the first expression, which is 𝑥, by each term of the second expression, which is 𝑥 + 2.
Here's how it's done step by step:
Step 1: Multiply the first term of the first expression, 𝑥, by the first term of the second expression, 𝑥:
𝑥 * 𝑥 = 𝑥^2
Step 2: Multiply the first term of the first expression, 𝑥, by the second term of the second expression, 2:
𝑥 * 2 = 2𝑥
Step 3: Multiply the second term of the first expression, -3, by the first term of the second expression, 𝑥:
-3 * 𝑥 = -3𝑥
Step 4: Multiply the second term of the first expression, -3, by the second term of the second expression, 2:
-3 * 2 = -6
Step 5: Combine all the results obtained in steps 1-4:
𝑥^2 + 2𝑥 - 3𝑥 - 6
Step 6: Simplify the final expression by combining like terms:
𝑥^2 - 𝑥 - 6
Therefore, the expanded and simplified form of (𝑥 − 3)(𝑥 + 2) is 𝑥^2 - 𝑥 - 6.