To find the product of the binomial (d+1) and the trinomial (–3d²–3d+2), we use the distributive property to multiply each term in the binomial by each term in the trinomial, combine like terms, and simplify to obtain –3d³ – 6d² – d + 2.
To find the product of the binomial (d+1) and the trinomial (–3d²–3d+2), we will apply the distributive property, also known as the FOIL method in this context. This means we will multiply each term in the first polynomial by each term in the second polynomial.
- Multiply d by each term in the trinomial: d * (–3d²) = –3d³, d * (–3d) = –3d², and d * 2 = 2d.
- Multiply 1 by each term in the trinomial: 1 * (–3d²) = –3d², 1 * (–3d) = –3d, and 1 * 2 = 2.
Now, combine the like terms:
–3d³ + (–3d² + –3d²) + (2d –3d) + 2
Simplifying this, we get:
–3d³ – 6d² – d + 2