Final answer:
To expand (x+2)(x-3), we use the distributive property to multiply each term of the first binomial by each term of the second, then combine like terms. The resulting expanded form is x² - x - 6.
Step-by-step explanation:
To expand the expression (x+2)(x-3), we use the distributive property, which is also known as the FOIL (First, Outer, Inner, Last) method in the context of binomials. The process involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.
Here's the step-by-step expansion:
- First, multiply the first terms of each binomial: x * x = x².
- Outer, multiply the outer terms: x * (-3) = -3x.
- Inner, multiply the inner terms: 2 * x = +2x.
- Last, multiply the last terms of each binomial: 2 * (-3) = -6.
Now combine the like terms:
x² (first terms) + (-3x) (outer terms) + 2x (inner terms) - 6 (last terms) = x² - x - 6.
So the expanded form of the expression (x+2)(x-3) is x² - x - 6.