(d+6)(2d^2-d+7)

Jasonbradley

2 min read

·

Jun 16, 2024

15

Share

Expanding the Expression: (d+6)(2d^2-d+7)

This expression represents the product of two polynomials: a binomial (d+6) and a trinomial (2d^2-d+7). To simplify this expression, we will use the distributive property, commonly known as FOIL (First, Outer, Inner, Last).

Using FOIL to Expand

1. First: Multiply the first terms of each polynomial:

• d * 2d^2 = 2d^3

2. Outer: Multiply the outer terms of each polynomial:

• d * 7 = 7d

3. Inner: Multiply the inner terms of each polynomial:

• 6 * 2d^2 = 12d^2

4. Last: Multiply the last terms of each polynomial:

• 6 * -d = -6d
• 6 * 7 = 42

Combining the Terms

Now, we combine all the terms we obtained:

2d^3 + 7d + 12d^2 - 6d + 42

Finally, we arrange the terms in descending order of their exponents:

2d^3 + 12d^2 + d + 42

Therefore, the expanded form of (d+6)(2d^2-d+7) is 2d^3 + 12d^2 + d + 42.