Expanding the Expression: (x+2)(x+3)
This expression involves multiplying two binomials. We can expand it using the FOIL method, which stands for First, Outer, Inner, Last.
Applying the FOIL Method

First: Multiply the first terms of each binomial: x * x = x²

Outer: Multiply the outer terms of the binomials: x * 3 = 3x

Inner: Multiply the inner terms of the binomials: 2 * x = 2x

Last: Multiply the last terms of each binomial: 2 * 3 = 6
Combining the Terms
Now, combine all the terms we obtained: x² + 3x + 2x + 6
Finally, combine the like terms (the terms with 'x'): x² + 5x + 6
Therefore, the expanded form of (x+2)(x+3) is x² + 5x + 6.