11 6 Special Binomial Products Perfect Square Binomial

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

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

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

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

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