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Lesson 2.3 FiNDING SPECIAL PRODUCTS OF POLYNOMIALS

Lesson 2.3 FiNDING SPECIAL PRODUCTS OF POLYNOMIALS. Essential Question. How do I use Special Product Patterns to Multiply Polynomials?. Review. Rules for Polynomials Adding When adding polynomials, combine like terms and write answer with degree in descending order.

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Lesson 2.3 FiNDING SPECIAL PRODUCTS OF POLYNOMIALS

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  1. Lesson 2.3FiNDING SPECIAL PRODUCTS OF POLYNOMIALS

  2. Essential Question How do I use Special Product Patterns to Multiply Polynomials?

  3. Review • Rules for Polynomials • Adding • When adding polynomials, combine like terms and write answer with degree in descending order. • (3x3 + 2x + 5) + (2x3 – x +10) = 5x3 + 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. • (3x3 + 2x + 5) - (2x3 – x +10) • (3x3 + 2x + 5) + (–2x3 + x – 10) = x3+ 3x - 5

  4. Review • Rules for Polynomials • Multiplying • When multiplying polynomials, MULTIPLY the coefficients and ADD the exponents. • 5x3(2x2 + 3x – 5) = 10x5 +15x4 – 25x3

  5. Special Products • Special Products – Square of Binomials • (a + b)2 = a2 + 2ab + b2 • 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 • x2 + 6x + 9 Step 3: Simplify

  6. Special Products • Special products – Square of Binomials • (a – b)2 = a2 – 2ab + b2 • 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 • 9x2 - 12x + 4 Step 3: Simplify

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

  8. Special Products • Special Products – Sum and Difference Pattern • (a + b)(a – b) = a2 – b2 • Example: • (x + 5)(x – 5) a b Step 1: Identify a and b • (x + 5)(x – 5) = x2 – 52 Step 2: Substitute = x2 – 25 Step 3: Simplify

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

  10. Assignment • Pg. 70 (1-18)

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