Expand and simplify the following product, using the distributive property:
(𝑥 − 3)(𝑥 + 2).
Using the distributive property:
(𝑥 − 3)(𝑥 + 2) = 𝑥(𝑥 + 2) − 3(𝑥 + 2)
= 𝑥² + 2𝑥 − 3𝑥 − 6
= 𝑥² − 𝑥 − 6
Therefore, the expanded and simplified product of (𝑥 − 3)(𝑥 + 2) is 𝑥² − 𝑥 − 6.
To expand and simplify the product (𝑥 − 3)(𝑥 + 2), we can use the distributive property.
Using the distributive property, we multiply each term in the first expression (𝑥 − 3) by each term in the second expression (𝑥 + 2).
First, multiply the first term of the first expression (𝑥) by each term in the second expression:
𝑥 * 𝑥 = 𝑥^2
𝑥 * 2 = 2𝑥
Next, multiply the second term of the first expression (-3) by each term in the second expression:
-3 * 𝑥 = -3𝑥
-3 * 2 = -6
Putting it all together, we have:
(𝑥 − 3)(𝑥 + 2) = 𝑥^2 + 2𝑥 - 3𝑥 - 6
Now, combine like terms:
𝑥^2 + 2𝑥 - 3𝑥 - 6 = 𝑥^2 - 𝑥 - 6
Therefore, the expanded and simplified form of (𝑥 − 3)(𝑥 + 2) is 𝑥^2 - 𝑥 - 6.