## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$$10t^4+3t^3-20t^2+\frac{9t}{2}-2$$
We do this problem like we did with the FOIL method. However, there now may be more than two terms per factor, so we cannot just multiply the first, outer, inner, and last terms together. Instead, we must be sure that all terms within both factors are multiplied by each other. Doing this, we find: $$\left(5t^2-t+\frac{1}{2}\right)\left(2t^2+t-4\right) \\ 5\cdot \:2t^2t^2+5t^2t-5\cdot \:4t^2-2t^2t-tt+4t+2\cdot \frac{1}{2}t^2+\frac{1}{2}t-4\cdot \frac{1}{2} \\ 10t^4+3t^3-20t^2+\frac{9t}{2}-2$$