Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
List of important publications in mathematics wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Location arithmetic wikipedia , lookup
Vincent's theorem wikipedia , lookup
Laws of Form wikipedia , lookup
System of polynomial equations wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
Factorization of polynomials over finite fields wikipedia , lookup
3-2 Multiplying Polynomials Warm Up Multiply. 1. x(x3) x4 2. 3x2(x5) 3x7 3. 2(5x3) 10x3 4. x(6x2) 6x3 5. xy(7x2) 7x3y 6. 3y2(–3y) –9y3 Holt McDougal Algebra 2 3-2 Multiplying Polynomials Objectives Multiply polynomials. Holt McDougal Algebra 2 3-2 Multiplying Polynomials Example 1: Multiplying a Monomial and a Polynomial Find each product. A. 4y2(y2 + 3) 4y2(y2 + 3) 4y2 y2 + 4y2 3 4y4 + 12y2 Distribute. Multiply. B. fg(f4 + 2f3g – 3f2g2 + fg3) fg(f4 + 2f3g – 3f2g2 + fg3) fg f4 + fg 2f3g – fg 3f2g2 + fg fg3 Distribute. f5g + 2f4g2 – 3f3g3 + f2g4 Multiply. Holt McDougal Algebra 2 3-2 Multiplying Polynomials To multiply any two polynomials, use the Distributive Property and multiply each term in the second polynomial by each term in the first. Holt McDougal Algebra 2 3-2 Multiplying Polynomials Example 2: Multiplying Polynomials Find the product. (a – 3)(2 – 5a + a2) (a – 3)(a2 – 5a + 2) Write polynomials in standard form. Distribute a and then –3. a(a2) + a(–5a) + a(2) – 3(a2) – 3(–5a) –3(2) a3 – 5a2 + 2a – 3a2 + 15a – 6 Multiply. Add exponents. a3 – 8a2 + 17a – 6 Holt McDougal Algebra 2 Combine like terms. 3-2 Multiplying Polynomials Example 3: Multiplying Polynomials Find the product. (y2 – 7y + 5)(y2 – y – 3) Multiply each term of one polynomial by each term of the other. Use a table to organize the products. y2 –y –3 The top left corner is the first 2 4 3 2 y y –y –3y term in the product. Combine terms along diagonals to get –7y –7y3 7y2 21y the middle terms. The bottom right corner is the last term in 5 2 5y –5y –15 the product. y4 + (–7y3 – y3 ) + (5y2 + 7y2 – 3y2) + (–5y + 21y) – 15 y4 – 8y3 + 9y2 + 16y – 15 Holt McDougal Algebra 2 3-2 Multiplying Polynomials CLASSWORK Worksheet Holt McDougal Algebra 2 3-2 Multiplying Polynomials CLASSWORK Worksheet Holt McDougal Algebra 2 3-2 Multiplying Polynomials Objectives Use binomial expansion to expand binomial expressions that are raised to positive integer powers. Holt McDougal Algebra 2 3-2 Multiplying Polynomials Notice the coefficients of the variables in the final product of (a + b)3. these coefficients are the numbers from the third row of Pascal's triangle. Each row of Pascal’s triangle gives the coefficients of the corresponding binomial expansion. The pattern in the table can be extended to apply to the expansion of any binomial of the form (a + b)n, where n is a whole number. Holt McDougal Algebra 2 3-2 Multiplying Polynomials Example 1: Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. A. (k – 5)3 1331 Identify the coefficients for n = 3, or row 3. 1(k)3 + 3(k)2(–5) + 3(k)(–5)2 + 1(–5)3 k3 – 15k2 + 75k – 125 B. (3x + 1)4 14641 Identify the coefficients for n = 4, or row 4. 1(3x)4 + 4(3x)3(1) + 6(3x)2(1)2 + 4(3x)(1)3 + 1(1)4 81x4 + 108x3 + 54x2 + 12x + 1 Holt McDougal Algebra 2 3-2 Multiplying Polynomials CLASSWORK Worksheet Holt McDougal Algebra 2