d) \( (2 x+3)(x-7) \)

To expand \( (2x + 3)(x - 7) \), apply the distributive property, also known as the FOIL method for binomials. First, multiply the first terms: \( 2x \cdot x = 2x^2 \). Next, multiply the outer terms: \( 2x \cdot (-7) = -14x \). Then, multiply the inner terms: \( 3 \cdot x = 3x \). Finally, multiply the last terms: \( 3 \cdot (-7) = -21 \). Combining these, you get \( 2x^2 - 14x + 3x - 21\), which simplifies to \( 2x^2 - 11x - 21 \). This algebraic expression is not just a bunch of symbols; it’s a powerful tool you can use in real-world scenarios! For instance, this type of polynomial can represent the area of a rectangular plot where the length and width are defined by linear expressions, making it useful in fields like architecture, landscaping, and real estate to calculate space efficiently.