How do I use Special Product Patterns to Multiply Polynomials?

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How do I use Special Product Patterns to Multiply Polynomials?

 Rules for Polynomials  Adding  When adding polynomials, combine like terms and write answer with degree in descending order.  (3x 3 + 2x + 5) + (2x 3 – x +10) = 5x 3 + x +15  Subtracting  When subtracting polynomials, distribute the minus sign through the following parenthesis. Then, combine like terms and write answer with degree in descending order.  (3x 3 + 2x + 5) - (2x 3 – x +10)  (3x 3 + 2x + 5) + (–2x 3 + x – 10) = x 3 + 3x - 5

 Rules for Polynomials  Multiplying  When multiplying polynomials, MULTIPLY the coefficients and ADD the exponents.  5x 3 (2x 2 + 3x – 5) = 10x 5 +15x 4 – 25x 3

 Special Products – Square of Binomials  (a + b) 2 = a 2 + 2ab + b 2  Example:  (x +3) 2 a b Step 1: Identify a and b  (x) 2 + 2(x)(3) + (3) 2 Step 2: Substitute values for a and b  x 2 + 6x + 9 Step 3: Simplify

 Special products – Square of Binomials  (a – b) 2 = a 2 – 2ab + b 2  Example:  (3x - 2) 2 a b Step 1: Identify a and b  (3x) 2 - 2(3x)(2) + (2) 2 Step 2: Substitute values for a and b  9x 2 - 12x + 4 Step 3: Simplify

 1. (y + 9) 2  2. (3z + 7) 2  3. (2w – 3) 2  4. (10 d – 3c) 2

 Special Products – Sum and Difference Pattern  (a + b)(a – b) = a 2 – b 2  Example:  (x + 5)(x – 5) a b Step 1: Identify a and b  (x + 5)(x – 5) = x 2 – 5 2 Step 2: Substitute = x 2 – 25 Step 3: Simplify

 1. (g + 10)(g – 10)  2. (7x + 1)(7x – 1)  3. (2h – 9)(2h + 9)  4. (6y + 3)(6y – 3)

 Pg. 70 (1-18)

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