Objective Find special products of binomials.

Check It Out! Example 1 Multiply. A. (x + 6)2 B. (a + 4)2 (x + 6)(x + 6) (x + 4)(x + 4) x2 + 4x + 4x + 42 x2 + 6x + 6x + 62 x2 + 8x + 16 x2 + 12x + 36 Do you see a pattern? (a + b)2 = a2 + 2ab + b2

Check It Out! Example 1 Multiply. A. (x + 7)2 Use the rule for (a + b)2. (a + b)2 = a2 + 2ab + b2 Identify a and b: a = x and b = 7. (x + 7)2 = x2 + 2(x)(7) + 72 = x2 + 14x + 49 Simplify. B. (5a + b)2 Use the rule for (a + b)2. (a + b)2 = a2 + 2ab + b2 Identify a and b: a = 5a and b = b. (5a + b)2 = (5a)2 + 2(5a)(b) + b2 = 25a2 + 10ab + b2 Simplify.

Example 2: Finding Products in the Form (a – b)2 Multiply. A. (x – 6)2 Use the rule for (a – b)2. (a – b)2 = a2 – 2ab + b2 Identify a and b: a = x and b = 6. (x – 6)2 = x2 – 2x(6) + (6)2 = x2 – 12x + 36 Simplify. B. (4m – 10)2 Use the rule for (a – b)2. Identify a and b: a = 4m and b = 10. (a – b)2 = a2 – 2ab + b2 (4m – 10)2 = (4m)2 – 2(4m)(10) + (10)2 = 16m2 – 80m + 100 Simplify.

Example 3: Finding Products in the Form (a + b)(a – b) Multiply. A. (x + 4)(x – 4) Use the rule for (a + b)(a – b). (a + b)(a – b) = a2 – b2 Identify a and b: a = x and b = 4. (x + 4)(x – 4) = x2 – 42 = x2 – 16 Simplify. B. (p2 + 8q)(p2 – 8q) Use the rule for (a + b)(a – b). (a + b)(a – b) = a2 – b2 Identify a and b: a = p2 and b = 8q. (p2 + 8q)(p2 – 8q) = p4 – (8q)2 = p4 – 64q2 Simplify.

Example 1C: Finding Products in the Form (a + b)2 Multiply. C. (5 + m2)2 Use the rule for (a + b)2. (a + b)2 = a2 + 2ab + b2 Identify a and b: a = 5 and b = m2. (5 + m2)2 = 52 + 2(5)(m2) + (m2)2 = 25 + 10m2 + m4 Simplify.

Example 2: Finding Products in the Form (a – b)2 Multiply. C. (2x – 5y)2 Use the rule for (a – b)2. (a – b)2 = a2 – 2ab + b2 Identify a and b: a = 2x and b = 5y. (2x – 5y)2 = (2x)2 – 2(2x)(5y) + (5y)2 = 2x2 – 20xy +25y2 Simplify.