Learning Objectives:

__Math Tutoring on Multiplying Polynomials__

To **multiply monomials**, we need to **multiply** the coefficients and then **multiply **the variables using the product rule for exponents as stated here. Remember, we are allowed to change the order of **multiple multiplication** due to the **commutative property of multiplication**. To **multiply **two** polynomials**, we **multiply** each term in one **polynomial** by each term in the other **polynomial** and then simplify by combining like terms in right and descending order. To two **binomials (a+b) **and** (c+d)** we apply **FOIL **method, where **F**irst terms: **ac**, **O**uter terms: **ad**, **I**nner terms: **bc**, **L**ast terms: **bd. **Another special product is the product of a sum and difference, like **(a+b) **and **(a-b).** The product of the sum and difference of the same two terms is the square of the first term minus the square of the second term. **(a+b)(a-b) = a² b²,** this is called a **Difference of squares. **There are special formulas for the **square **of **binomials: (a+b)² = a² + 2ab + b² **and** (a-b)² = a² - 2ab + b² .**

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**Hook Questions:**

*1. **How do you multiply a monomial by a monomial?*

*2. **How do you multiply a binomial by a binomial?*

*3. **How do you multiply a trinomial by a trinomial?*

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