Answer:
The distributive property is a fundamental property of arithmetic that applies to multiplying two expressions. It states that the product of a sum or difference of two numbers with a third number is equal to the sum or difference of the products of each term of the first expression with the third number.
In the context of multiplying two polynomials, the distributive property is used to simplify the product by breaking it down into smaller products. Specifically, when multiplying a polynomial by another polynomial, you need to distribute each term of one polynomial to every term in the other polynomial.
For example, let's say you want to multiply the polynomials (2x + 3) and (x - 1):
(2x + 3) * (x - 1)
Using the distributive property, you distribute the first term of the first polynomial (2x) to every term in the second polynomial (x and -1) and then add that to the product of the second term of the first polynomial (3) and every term in the second polynomial:
= 2x * x + 2x * (-1) + 3 * x + 3 * (-1)
Simplifying each term gives:
= 2x^2 - 2x + 3x - 3
= 2x^2 + x - 3
So the product of the two polynomials is 2x^2 + x - 3.