Sure, let's do this step by step.
Given the expressions are:
- Expression 1: 2x + 5y + 3
- Expression 2: 2x + 5y + 4
We want to find the product of these expressions. We can do this by using the distributive property of multiplication which states that a(b+c) = ab + ac.
1. Multiply each term in the first expression with each term in the second expression:
(2x * 2x) + (2x * 5y) + (2x * 4) + (5y * 2x) + (5y * 5y) + (5y * 4) + (3 * 2x) + (3 * 5y) + (3 * 4)
2. This simplifies to:
4x^2 + 10xy + 8x + 10xy + 25y^2 + 20y + 6x + 15y + 12
3. Combine similar terms:
4x^2 + 20xy + 14x + 25y^2 + 35y + 12
So, the product of (2x+5y+3) and (2x+5y+4) is 4x^2 + 20xy + 14x + 25y^2 + 35y + 12.