7. Multiply: \( \left(3 x^{2}-4\right)\left(4 x^{2}-9 y\right) \)

To multiply the expressions \( (3x^{2} - 4)(4x^{2} - 9y) \), we can use the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first polynomial by each term in the second polynomial. 1. First, multiply the first terms: \( 3x^{2} \cdot 4x^{2} = 12x^{4} \). 2. Next, multiply the outer terms: \( 3x^{2} \cdot -9y = -27xy \). 3. Then, multiply the inner terms: \( -4 \cdot 4x^{2} = -16x^{2} \). 4. Lastly, multiply the last terms: \( -4 \cdot -9y = 36y \). Now, combine all these results together: \[ 12x^{4} - 27xy - 16x^{2} + 36y \] So, the final result of the multiplication is: \[ 12x^{4} - 16x^{2} - 27xy + 36y \]