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Special Products

Lesson 7-8: Special Products SOL A.2b. Special Products. Objectives. Find squares of sums and differences. Find the product of a sum and a difference. Square of a Sum. Square of a Sum. Square of a Sum ( a + b ) 2 = a 2 + 2 a b + b 2 (3x + 5) 2 = (3x) 2 + 2 (3x) (5) + 5 2

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Special Products

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  1. Lesson 7-8: Special Products SOL A.2b Special Products

  2. Objectives • Find squares of sums and differences. • Find the product of a sum and a difference.

  3. Square of a Sum

  4. Square of a Sum Square of a Sum (a + b)2 = a2 + 2ab + b2 (3x + 5)2 = (3x)2 + 2(3x)(5) + 52 = 9x2 + 30x + 25 FOIL Method (3x + 5)(3x + 5) = 3x(3x) + 3x(5) + 5(3x) + 5(5) = 9x2 + 15x + 15x + 25 = 9x2 + 30x + 25

  5. Square of a Sum Square of a Sum (a + b)2 = a2 + 2ab + b2 (3x + 4y)2 = (3x)2 + 2(3x)(4y)+ (4y)2 = 9x2 + 24xy + 16y2 FOIL Method (3x + 4y)(3x + 4y) = 3x(3x) + 3x(4y) + 4y(3x) + 4y(4y) = 9x2 + 12xy + 12xy + 16y2 = 9x2 + 24xy + 16y2

  6. Practice Time! • Turn to page 455 and work problems 1, 3, and 6 on your own.

  7. Square of a Difference

  8. Square of a Difference Square of a Difference (a– b)2= a2– 2ab+ b2 (2x – 5y)2 = (2x)2 – 2(2x)(5y) + (5y)2 = 4x2 – 20xy + 25y2 FOIL Method (2x – 5y)(2x – 5y) = 2x(2x) + 2x(-5y) + (-5y)(2x) + (-5y)(-5y) = 4x2 + (-10xy) + (-10xy) + 25y2 = 4x2 – 20xy + 25y2

  9. Square of a Difference Square of a Difference (a – b)2 = a2 – 2ab + b2 (a – 2b)2 = a2 – 2(a)(2b) + (2b)2 = a2 – 4ab + 4b2 FOIL Method (a – 2b)(a – 2b) = a(a) + a(-2b) + (-2b)(a) + (-2b)(-2b) = a2 + (-2ab) + (-2ab) + 4b2 = a2 – 4ab + 4b2

  10. Practice Time! • Turn to page 455 and work problems 2, 4, and 5 on your own.

  11. Product of a Sum and a Difference

  12. Product of a Sum and a Difference Product of a Sum and a Difference: (a + b)(a– b) = a2– b2 (2x2 + 3)(2x2 – 3) = (2x2)2 – (3)2 = 4x4 – 9 FOIL Method = 2x2(2x2) + 2x2(-3) + 3(2x2) + 3(-3) = 4x4 + (-6x2) + 6x2 + (-9) = 4x4 – 9

  13. Product of a Sum and a Difference Product of a Sum and a Difference: (a + b)(a – b) = a2 – b2 (4c – 7d)(4c + 7d) = (4c)2 – (7d)2 = 16c2 – 49d2 FOIL Method = 4c(4c) + 4c(7d) + (-7d)(4c) + (-7d)(7d) = 16c2 + 28cd + (-28cd) – 49d2 = 16c2 – 49d2

  14. Practice Time! • Turn to page 455 and work problems 8, 9, and 10 on your own.

  15. Homework! • Page 455 (1 – 47 odd; 62 – 65 all).

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