b) \( 2(a+b)^{2}-3(a-b)^{2}= \)

Let's simplify the expression step by step! Start with the expansion of each square: First, expand \( (a + b)^2 = a^2 + 2ab + b^2 \) and \( (a - b)^2 = a^2 - 2ab + b^2 \). Now, substituting these back into the expression gives: \[ 2(a+b)^{2} - 3(a-b)^{2} = 2(a^2 + 2ab + b^2) - 3(a^2 - 2ab + b^2) \] Distributing the coefficients, we have: \[ = 2a^2 + 4ab + 2b^2 - 3a^2 + 6ab - 3b^2 \] Now combine like terms: \[ = (2a^2 - 3a^2) + (4ab + 6ab) + (2b^2 - 3b^2) \] \[ = -a^2 + 10ab - b^2 \] So, the final simplified expression is: \[ -a^2 + 10ab - b^2 \]