Expand and simplify the following product, using the distributive property:
(𝑥 − 3)(𝑥 + 2).
Using the distributive property, we get:
(𝑥 − 3)(𝑥 + 2) = 𝑥(𝑥) + 𝑥(2) − 3(𝑥) − 3(2)
Simplifying, we get:
𝑥² + 2𝑥 − 3𝑥 − 6
Combining like terms:
𝑥² − 𝑥 − 6
Therefore, (𝑥 − 3)(𝑥 + 2) = 𝑥² − 𝑥 − 6.
To expand and simplify the given product, we can use the distributive property. The distributive property states that for any real numbers a, b, and c:
(a + b)c = ac + bc
Using this property, we can expand the given product as follows:
(x - 3)(x + 2) = x(x) + x(2) - 3(x) - 3(2)
Now, let's simplify each term:
x(x) = x^2
x(2) = 2x
-3(x) = -3x
-3(2) = -6
Putting it all together, the simplified form of the given product is:
x^2 + 2x - 3x - 6
Combining like terms, we get:
x^2 - x - 6
So, (x - 3)(x + 2) expands and simplifies to x^2 - x - 6.