(a-2)(a+5)+(a+3)(a-4)

To solve the given expression, (a-2)(a+5)+(a+3)(a-4), we can apply the distributive property, which states that when multiplying two binomials, you distribute each term from the first binomial to each term in the second binomial.

Let's break it down step by step:

1. Multiply (a-2) by (a+5): (a-2)(a+5) = a(a) + a(5) - 2(a) - 2(5) = a^2 + 5a - 2a - 10 = a^2 + 3a - 10

2. Multiply (a+3) by (a-4): (a+3)(a-4) = a(a) + a(-4) + 3(a) + 3(-4) = a^2 - 4a + 3a - 12 = a^2 - a - 12

3. Put the results together: (a-2)(a+5) + (a+3)(a-4) = a^2 + 3a - 10 + a^2 - a - 12 = 2a^2 + 2a - 22

Thus, the simplified expression is 2a^2 + 2a - 22.