Question

Simplify the expression: \( (3x - 2)(2x + 5) \)

Answer 1

Distributive Property: Multiply each term in the first bracket by each term in the second bracket.

1. First terms: \(3x \cdot 2x = 6x^2\).
2. Outer terms: \(3x \cdot 5 = 15x\).
3. Inner terms: \((-2) \cdot 2x = -4x\).
4. Last terms: \((-2) \cdot 5 = -10\).

Now combine like terms:

\[ (3x - 2)(2x + 5) = 6x^2 + 15x - 4x - 10 = 6x^2 + (15x - 4x) - 10 = 6x^2 + 11x - 10. \]

Final Answer: \(\boxed{6x^2 + 11x - 10}\)

Short Explanation (Why this works)

The distributive property states that \(a(b+c) = ab + ac\). Here, \(a = 3x - 2\), \(b = 2x\), and \(c = 5\). So: \[ (3x - 2)(2x + 5) = (3x - 2)\cdot 2x + (3x - 2)\cdot 5. \] Expanding and simplifying gives \(6x^2 + 11x - 10\).