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Multiplying Binomials

Multiplying Binomials. Objectives: To Multiply Two Binomials FOIL To multiply the sum and difference of two expressions To square a binomial. Example 1. Multiply. (x + 2)(x + 3). FOIL. u t s i d e. i n s i d e. a s t. i r s t. = (x)(x) +. (x)(3) +. (2)(x) +.

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Multiplying Binomials

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  1. Multiplying Binomials Objectives: To Multiply Two Binomials FOIL To multiply the sum and difference of two expressions To square a binomial

  2. Example 1 Multiply. (x + 2)(x + 3) FOIL u t s i d e i n s i d e a s t i r s t = (x)(x) + (x)(3) + (2)(x) + (2)(3) = x2 + 3x + 2x + 6 = x2 + 5x + 6

  3. Example 2 Multiply. (3x + 2)(x + 5) = (3x)(x) + (3x)(5) + (2)(x) + (2)(5) = 3x2 + 15x + 2x + 10 = 3x2 + 17x + 10

  4. Example 3 Multiply. (4ab + 3)(2a2b + 1) = (4ab)(2a2b) + (4ab)(1) + (3)(2a2b) + (3)(1) = 8a3b2 + 4ab + 6a2b + 3

  5. Practice 1 Multiply. 1) (x + 3)(x + 4) 2) (x + 3)(x – 5) 3) (2x + 1)(x + 4)

  6. Practice 2 Multiply. 4) (2x2 – 3)(x – 2) 5) (6x2 + 5)(2x3 + 1) 6) (2xy + 4x)(-2y + y2)

  7. Multiplying Binomials – Special Products Objectives: To multiply the sum and difference of two expressions To square a binomial

  8. Example 1 Multiply. (x + 6)(x – 6) = (x)(x) + (x)(-6) + (6)(x) + (6)(-6) = x2 – 6x + 6x - 36 = x2 - 36

  9. Example 2 Multiply. (2x + 4)(2x – 4) = (2x)(2x) + (2x)(-4) + (4)(2x) + (4)(-4) = 4x2 – 8x + 8x - 16 = 4x2 - 16

  10. Example 3 Multiply. (-3x + 4y)(-3x – 4y) = (-3x)(-3x) + (-3x)(-4y) + (4y)(-3x) + (4y)(-4y) = 9x2 + 12xy – 12xy – 16y2 = 9x2 – 16y2

  11. Practice Multiply. 1) (x + 2)(x – 2) 2) (x2 + 7)(x2 – 7) 3) (3x + 5)(3x – 5)

  12. Example 4 Multiply. (x + 2)2 = (x + 2)(x + 2) = (x)(x) + (x)(2) + (2)(x) + (2)(2) = x2 + 2x + 2x + 4 = x2 + 4x + 4

  13. Example 5 Multiply. (x - 3)2 = (x - 3)(x - 3) = (x)(x) + (x)(-3) + (-3)(x) + (-3)(-3) = x2 - 3x - 3x + 9 = x2 - 6x + 9

  14. Example 6 Multiply. (2x – 3y)2 = (2x – 3y)(2x – 3y) = (2x)(2x) + (2x)(-3y) + (-3y)(2x) + (-3y)(-3y) = 4x2 - 6xy - 6xy + 9y2 = 4x2 - 12xy + 9y2

  15. Practice Multiply. 1) (x + 3)2 2) (2x + 1)2 3) (2y + 4x)2

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