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Multiplying Polynomials • How do we multiply polynomials? •How do we use binomial expansion to expand binomial expressions that are raised to positive integer powers? Holt McDougal Algebra 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 Multiplying Polynomials This information is formalized by the Binomial Theorem, which you will study further in Chapter 11. Holt McDougal Algebra 2 Multiplying Polynomials Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. 1. (k – 5)3 Identify the coefficients for n = 3, or row 3. 1331 [1(k)3(–5)0] + [3(k)2(–5)1] + [3(k)1(–5)2] + [1(k)0(–5)3] k 1 5k 7 5 k 125 2 3 2. (6m – 8)3 Identify the coefficients for n = 3, or row 3. 1331 [1(6m)3(–8)0] + [3(6m)2(–8)1] + [3(6m)1(–8)2] + [1(6m)0(–8)3] 216m 864m 1152 m 512 3 Holt McDougal Algebra 2 2 Multiplying Polynomials Using Pascal’s Triangle to Expand Binomial Expressions Expand each expression. 3. (x + 2)3 1 3 3 1 Identify the coefficients for n = 3, or row 3. [1(x)3(2)0] + [3(x)2(2)1] + [3(x)1(2)2] + [1(x)0(2)3] 2 3 x 6 x 12 x 8 4. (x – 4)5 1 5 10 10 5 1 Identify the coefficients for n = 5, or row 5. [1(x)5(–4)0] + [5(x)4(–4)1] + [10(x)3(–4)2] + [10(x)2(–4)3] + [5(x)1(–4)4] + [1(x)0(–4)5] x 20 x 160 x 640 x 1 2 8 0 x 1024 5 4 Holt McDougal Algebra 2 3 2 Multiplying Polynomials Using Pascal’s Triangle to Expand Binomial Expressions Expand the expression. 5. (3x + 1)4 Identify the coefficients for n = 4, or row 4. 14641 [1(3x)4(1)0] + [4(3x)3(1)1] + [6(3x)2(1)2] + [4(3x)1(1)3] + [1(3x)0(1)4] 81x 108 x 54 x 12 x 1 4 Holt McDougal Algebra 2 3 2 Multiplying Polynomials Lesson 3.2 Practice C Holt McDougal Algebra 2