a) \( (x-3)(x+3) \) b) \( (x+7)^{2} \) c) \( (2 x+3 y)\left(4 x^{2}-6 x y+9 y^{2}\right) \)

It looks like you have three algebraic expressions, and I'll assume you'd like them simplified or expanded. Here's how each one can be handled: ### a) \( (x - 3)(x + 3) \) This is a product of two conjugates, which follows the difference of squares formula: \[ (a - b)(a + b) = a^2 - b^2 \] Applying this to your expression: \[ (x - 3)(x + 3) = x^2 - 3^2 = x^2 - 9 \] **Simplified Form:** \[ x^2 - 9 \] --- ### b) \( (x + 7)^2 \) This is a perfect square trinomial, which can be expanded using the formula: \[ (a + b)^2 = a^2 + 2ab + b^2 \] Applying this to your expression: \[ (x + 7)^2 = x^2 + 2(x)(7) + 7^2 = x^2 + 14x + 49 \] **Expanded Form:** \[ x^2 + 14x + 49 \] --- ### c) \( (2x + 3y)\left(4x^2 - 6xy + 9y^2\right) \) Notice that the second polynomial inside the parentheses resembles the form \( a^2 - ab + b^2 \), which is part of the sum of cubes factorization: \[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \] Here, \( a = 2x \) and \( b = 3y \). Therefore: \[ (2x + 3y)\left(4x^2 - 6xy + 9y^2\right) = (2x)^3 + (3y)^3 = 8x^3 + 27y^3 \] **Expanded Form:** \[ 8x^3 + 27y^3 \] --- ### Summary - **a)** \( (x - 3)(x + 3) = x^2 - 9 \) - **b)** \( (x + 7)^2 = x^2 + 14x + 49 \) - **c)** \( (2x + 3y)(4x^2 - 6xy + 9y^2) = 8x^3 + 27y^3 \) If you had a different intention for these expressions, please provide more details, and I'd be happy to assist further!