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Essential Questions. How do we multiply polynomials? How do we use binomial expansion to expand binomial expressions that are raised to positive integer powers?. To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.
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Essential Questions • How do we multiply polynomials? • How do we use binomial expansion to expand binomial expressions that are raised to positive integer powers?
To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents.
Example 1: Multiplying a Monomial and a Polynomial Find each product. Distribute. Distribute.
Example 1: Multiplying a Monomial and a Polynomial Find each product. Distribute. Distribute.
To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first. Keep in mind that if one polynomial has m terms and the other has n terms, then the product has mn terms before it is simplified.
Example 2A: Multiplying Polynomials Find the product. Method 1 Multiply horizontally. Write polynomials in standard form. Distribute a and then –3. a(a2) + a(–5a)+ a(2) – 3(a2) – 3(–5a) –3(2) Multiply. Add exponents. Combine like terms.
Example 2B: Multiplying Polynomials Find the product. Method 2 Multiply vertically. Write each polynomial in standard form. Multiply (a2 – 5a + 2) by –3. Multiply (a2 – 5a + 2) by a, and align like terms. Combine like terms.
y2 –y–3 y2 –7y 5 Example 3: Multiplying Polynomials Find the product. Multiply each term of one polynomial by each term of the other. Use a table to organize the products. The top left corner is the first term in the product. Combine terms along diagonals to get the middle terms. The bottom right corner is the last term in the product.
Example 4: Multiplying Polynomials Find the product. Method 1 Multiply horizontally. Write polynomials in standard form. Distribute 3b and then –2c. 3b(3b2) + 3b(–2c2)+ 3b(–bc) – 2c(3b2) – 2c(–2c2) – 2c(–bc) Multiply. Add exponents. Combine like terms.
x2 –4x1 x2 5x – 2 Example 5: Multiplying Polynomials Find the product. Multiply each term of one polynomial by each term of the other. Use a table to organize the products. The top left corner is the first term in the product. Combine terms along diagonals to get the middle terms. The bottom right corner is the last term in the product.
