Question

Find the product for:
(2k²-6k+9)(k+3)

Answer 1

The product of the expression (2k²-6k+9)(k+3) can be found by applying the FOIL method, resulting in the final simplified expression 2k³ - 9k + 27.

Step-by-step explanation:

To find the product of the expression (2k²-6k+9)(k+3), you need to apply the distributive property, also known as the FOIL method, which stands for First, Outside, Inside, Last. This means you multiply each term in the first polynomial by each term in the second polynomial.

1. Multiply the First terms: 2k² * k = 2k³.
2. Multiply the Outside terms: 2k² * 3 = 6k².
3. Multiply the Inside terms: -6k * k = -6k².
4. Multiply the Last terms: -6k * 3 = -18k.
5. Finally, multiply the middle term of the trinomial by the last term of the binomial: 9 * k = 9k, and 9 * 3 = 27.

Next, you combine like terms to form the final expression:

​​2k³ + (6k² - 6k²) + (9k - 18k) + 27

This simplifies to:

2k³ + -9k + 27

So the product of (2k²-6k+9)(k+3) is 2k³ - 9k + 27.