9. \( (2 x+3 y)^{2}-9 \)

To simplify or factor the expression \( (2x + 3y)^2 - 9 \), you can approach it in two ways: **expanding** the expression or **factoring** it using the difference of squares formula. ### 1. Expanding the Expression First, expand the squared term: \[ (2x + 3y)^2 = (2x)^2 + 2 \cdot (2x) \cdot (3y) + (3y)^2 = 4x^2 + 12xy + 9y^2 \] Now, subtract 9 from the expanded form: \[ 4x^2 + 12xy + 9y^2 - 9 \] So, the expanded form of \( (2x + 3y)^2 - 9 \) is: \[ 4x^2 + 12xy + 9y^2 - 9 \] ### 2. Factoring the Expression Notice that \( (2x + 3y)^2 - 9 \) is a **difference of squares**, which follows the formula: \[ a^2 - b^2 = (a - b)(a + b) \] Here, \( a = 2x + 3y \) and \( b = 3 \). Applying the formula: \[ (2x + 3y)^2 - 3^2 = (2x + 3y - 3)(2x + 3y + 3) \] So, the factored form of \( (2x + 3y)^2 - 9 \) is: \[ (2x + 3y - 3)(2x + 3y + 3) \] ### Summary - **Expanded Form:** \( 4x^2 + 12xy + 9y^2 - 9 \) - **Factored Form:** \( (2x + 3y - 3)(2x + 3y + 3) \) Depending on your needs, you can use either form for further calculations or simplifications.