Final answer:
The expression (7v-6)(2v²+5v+3) simplifies to 14v³ + 23v² - 18 using the distributive property, combining like terms after multiplying each term in the first polynomial by each term in the second.
Step-by-step explanation:
To simplify the expression (7v-6)(2v²+5v+3), we need to use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to multiply each term in the first polynomial by each term in the second polynomial.
- First: Multiply the first terms in each binomial: 7v * 2v² = 14v³.
- Outer: Multiply the outer terms: 7v * 5v = 35v².
- Inner: Multiply the inner terms: -6 * 2v² = -12v².
- Last: Multiply the last terms in each binomial: -6 * 3 = -18.
Now we add up all the products:
14v³ + (35v² - 12v²) + (-18)
Simplify the like terms:
14v³ + 23v² - 18
This is the simplified form of the given expression.