1. The problem is to analyze the expressions (2x + 5) and (4x - 3). 2. We can explore their sum, difference, product, or quotient depending on the question, but since none is specified, let's find their sum and product as common operations. 3. Sum: Use the formula for addition of polynomials: $$ (2x + 5) + (4x - 3) = 2x + 5 + 4x - 3 $$ 4. Combine like terms: $$ (2x + 4x) + (5 - 3) = 6x + 2 $$ 5. Product: Use distributive property (FOIL) for multiplication: $$ (2x + 5)(4x - 3) = 2x \cdot 4x + 2x \cdot (-3) + 5 \cdot 4x + 5 \cdot (-3) $$ 6. Calculate each term: $$ 8x^2 - 6x + 20x - 15 $$ 7. Combine like terms: $$ 8x^2 + 14x - 15 $$ 8. So, the sum of the expressions is $$6x + 2$$ and the product is $$8x^2 + 14x - 15$$.