# Exponents and Polynomial Multiplication

**Positive Integral Exponents**
- If n is a positive integer and x is a real number, then n factors of x equals to x multiply n times, where x is the base and n is the power or the exponent.

**Example**

**Exponents Property of Multiplication**

**Example**

**Exponents Property of Power of a Power**

**Example**

**Exponents Property of Power of a Product**

**Example**

**Exponents Property of Power of a Quotient**

**Example**

**Exponents Property of Division**

**Example**

**Zero as an Exponent**

**Example**

**Negative Integer Exponents**

**Example**

**Product of two Monomials**
- The product of two monomials made by regroup the coeffcients and variables, then multiplying the coefficients, and similar base by adding
their exponents, if there is a variable whose similar term is not exist, then keep this variable as a factor of the product.

**Example**

**Product of Monomial and Polynomial**
- To multiply a polynomial by a monomial, multiply each term of the polynomial by the monomial. This fundamental law is known as the distributive law.

**Example**

**Product of Two Polynomials**
- To multiply polynomials by each other follow the procedure:
- 1. Arrange each polynomial in decending order.
- 2. Multiply each term of one polynomial by each term of the other polynomial.
- 3. Add like terms.

**Example**

**The law of a square minus b square**
- The law of a square minus b square is the products of a plus b and a minus b, in which a, b are real numbers.

**Example**

**Square a Binomial**
- The square of a binomial is the sum of the square of the first term, twice the product of the two terms, and the square of the second term.

**Example**

**Special Products**

**Example**