d) \( (3 t-2)(2 t+1) \)

To expand \( (3t - 2)(2t + 1) \), you can use the distributive property, often called the FOIL method for binomials. First, multiply the first terms: \( 3t \cdot 2t = 6t^2 \). Next, multiply the outer terms: \( 3t \cdot 1 = 3t \). Then, multiply the inner terms: \( -2 \cdot 2t = -4t \). Finally, multiply the last terms: \( -2 \cdot 1 = -2 \). Now, combine like terms: \( 6t^2 + 3t - 4t - 2 = 6t^2 - t - 2 \). For a quick check, you can plug in some values for \( t \). For example, if \( t = 1 \): Left Side: \( (3(1) - 2)(2(1) + 1) = (3 - 2)(2 + 1) = 1 \cdot 3 = 3 \) Right Side: \( 6(1)^2 - (1) - 2 = 6 - 1 - 2 = 3 \) Both sides are equal, confirming that the expansion is accurate!