2. © William James Calhoun, 2001 9-8: Special Products OBJECTIVES: The student will use three patterns to find three special products. Three new tools in this section supposedly designed to make multiplying certain binomials easier. In fact, these tools eliminate only one or two steps from the information in section 9-7. Where these special product tools are going to be really helpful is in the next chapter on Factoring. For now, we will add them to our toolbox and use them for multiplying.

3. © William James Calhoun, 2001 9-8: Special Products 9.8.1: Square of a Sum (a + b) 2 = (a + b)(a + b) = a 2 + 2ab + b 2 EXAMPLE 1: Find each product. A. (y + 7) 2 B. (6p + 11q) 2 You could use FOIL, but let us use 9.8.1.Again, you could use FOIL, but let us use 9.8.1. (a + b) 2 = a 2 + 2ab + b 2 Take the first term and square it. Multiply the first and second terms and multiply by two. Take the second term and square it. (y + 7) 2 =y2y2 2(y)(7)+7272 + Clean up the answer. (y + 7) 2 = y 2 + 14y + 49 (a + b) 2 = a 2 + 2ab + b 2 Take the first term and square it. Multiply the first and second terms and multiply by two. Take the second term and square it. (6p + 11q) 2 =(6p) 2 2(6p)(11q)+(11q) 2 + Clean up the answer. (6p + 11q) 2 = 36p 2 + 132pq + 121q 2

4. © William James Calhoun, 2001 9-8: Special Products 9.8.2: Square of a Difference (a - b) 2 = (a - b)(a - b) = a 2 - 2ab + b 2 EXAMPLE 2: Find each product. A. (r - 6) 2 B. (4x 2 - 7t) 2 You could use FOIL, but let us use 9.8.2.Again, you could use FOIL, but let us use 9.8.2. (a - b) 2 = a 2 - 2ab + b 2 Take the first term and square it. Multiply the first and second terms and multiply by two. Take the second term and square it. (r - 6) 2 =r2r2 2(r)(6)-(6) 2 + Clean up the answer. (r - 6) 2 = r 2 - 12r + 36 (a + b) 2 = a 2 + 2ab + b 2 Take the first term and square it. Multiply the first and second terms and multiply by two. Take the second term and square it. (4x 2 - 7t) 2 =(4x 2 ) 2 2(4x 2 )(7t)-(7t) 2 + Clean up the answer. (4x 2 - 7t) 2 = 16x 4 - 56x 2 t + 49t 2

5. © William James Calhoun, 2001 9-8: Special Products 9.8.3: Difference of Squares (a + b)(a - b) = (a - b)(a + b) = a 2 - b 2 EXAMPLE 3: Find each product. A. (m - 2n)(m + 2n)B. (0.3t + 0.25w 2 )(0.3t - 0.25w 2 ) You could use FOIL, but let us use 9.8.3.Again, you could use FOIL, but let us use 9.8.3. (a - b)(a + b) = a 2 - b 2 Take the first term and square it. Write a minus sign. Take the second term and square it. (m - 2n)(m + 2n) =m2m2 -(2n) 2 Clean up the answer. (m - 2n)(m + 2n) = m 2 - 4n 2 (a + b)(a - b) = a 2 - b 2 Take the first term and square it. Write a minus sign. Take the second term and square it. () =(0.3t) 2 -(0.25w 2 ) 2 Clean up the answer. () = 0.09t 2 - 0.0625w 4

6. © William James Calhoun, 2001 9-8: Special Products HOMEWORK Page 546 #13 - 31 odd