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11-6 Special Binomial Products

11-6 Special Binomial Products. Perfect Square Binomial. 2. (a + b). = (a + b)(a + b). 2. = a. + ab. + ab. + b. 2. = a + 2ab + b. 2. 2. Notice:. 1.The ____ and ________ of the binomial are ________. first. last term. squared. 2.The ____________ is ____ the _______

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11-6 Special Binomial Products

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  1. 11-6 Special Binomial Products Perfect Square Binomial 2 (a + b) = (a + b)(a + b) 2 = a + ab + ab + b 2 = a + 2ab + b 2 2 Notice: 1.The ____ and ________ of the binomial are ________. first last term squared 2.The ____________ is ____ the _______ of the _________________ product middle term twice first and last term. 2 2 The answer will _______ be ______. NEVER a + b

  2. Difference of two Squares Pattern (a - b)(a + b) = a - ab + ab - b 2 2 = a - b 2 2 Notice: 1. The ____ and ________ of the binomial are ________. first last term squared no middle term 2. There is _____________ because the Outside and Inside terms of foil cancel because they are opposites. 2 2 The answer will _______ be _____. NEVER a + b

  3. 1. Expand (2n - 5)² 4n² - 20n + 25 (2n·-5) , 3rd (-5)² 2nd 2 Think: (2n)² , 1st This can only be done when the __________ are ________ . 2 binomials identical 2. Multiply (10n - 7)(10n + 7) 100n² - 49 -(7)² Think: (10n)² , This can only be done when ________ areand _________ are _________. 1st terms = last terms opposites

  4. 3. Compute 51² in your head. (50 + 1)² What they are referring to is rewrite as a _______________ and then compute. 50² + 50·1 + 1² 2· 2500 + 100+ 1 Why didn’t I use (60-9)? binomial squared 2601 4. Compute 89 · 91 in your head. (90-1)(90+1) What they are referring to is rewrite as the ____________ ________________ __________________. Why didn’t I use (80+9) & (80 + 11)? - 1² 90² product of 2 binomials and use difference of squares 8100 - 1 8099

  5. 5. The length of the side of a square is 4d + 3. a. Write the area of this square in expanded form. b. Draw the square and show how the expanded form relates to the figure. A = s² A = (4d + 3)² A = (4d)² +2(4d·3) + 3² 4d 3 A = 16d² + 24d + 9 16d² 12d 4d The sum of the 4 smaller squares is 3 12d 9 16d² (12d) + 2 + 9 = 16d² + 24d + 9 expanded form

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