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Multiply Binomials

Multiply Binomials. (ax + b)(cx +d) (ax + by)(cx +dy). - ( x - 9 ) ≤ 5 -1 -1 x - 9 ≥ -5 +9 +9 x ≥ 4. + ( x - 9) ≤ 5 x - 9 ≤ 5 +9 +9 x ≤ 14. What kind of statement?. | x - 9 | ≤ 5. less than is an “and” statement. Neg. Pos.

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Multiply Binomials

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  1. Multiply Binomials (ax + b)(cx +d) (ax + by)(cx +dy)

  2. - ( x - 9 ) ≤ 5 -1 -1 x - 9 ≥ -5 +9 +9 x ≥ 4 + ( x - 9) ≤ 5 x - 9 ≤ 5 +9 +9 x ≤ 14 What kind of statement? | x - 9 | ≤ 5 less than is an “and” statement Neg. Pos. Don’t forget To flip symbol Write as one inequality 4 ≤ x and x ≤ 14 4 ≤ x ≤14 Graph

  3. Graph 4 ≤ x ≤14 What kind of Circles? Now shade Between the circles !! <---|---|---|---|---|---|---|---|---|---> 2 4 6 8 10 12 14 16 18

  4. I = PRT 360= 360 = (2,000)(4)R 360 = 8,000 R 8,000 8,000 0.045 = R 4.5% = R Interest paid by bank Principle (invested) Rate is unknown Time is 4 years Regroup & Multiply Divide Change to % 6. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $2,000 accumulate $360 of interest in the checking accounting after 4 years, what was the annual simple interest rate on the savings account? (2,000) (R) (4)

  5. 1. (3x + 4)(5x +1) Distribute the 3x Multiply (don’t forget to add exponents when multiplying) Distribute the 4 Like terms add-same sign coefficients only (don’t add exp.) FOIL or use Distributive Property

  6. #2) (2x + 5)(3x +7) Distribute the 2x Multiply (don’t forget to add exponents when multiplying) Distribute the 5 Like terms add-same sign coefficients only (don’t add exp.) FOIL or use Distributive Property

  7. #3) (4x + 5)(3x -8) Distribute the 4x Multiply (don’t forget to add exponents when multiplying) Distribute the 5 like terms subtract- opposite signs coefficients only (don’t add exp.) FOIL or use Distributive Property =12x2 - 32x +15x - 40 =12x2 – 17x - 40

  8. #4) (3x - 2)(5x + 3) Distribute the 3x Multiply (don’t forget to add exponents when multiplying) Distribute the -2 like terms subtract- opposite signs coefficients only (don’t add exp.) FOIL or use Distributive Property =15x2 +9x - 10x - 6 =15x2 – 1x - 6

  9. #5) (3x - 2)(2x - 7) Distribute the 3x Multiply (don’t forget to add exponents when multiplying) Distribute the -2 like terms Add- same signs coefficients only (don’t add exp.) FOIL or use Distributive Property =6x2 - 21x - 4x + 14 =6x2 – 25x + 14

  10. #6) (4x - 8)(2x - 3) Distribute the 4x Multiply (don’t forget to add exponents when multiplying) Distribute the -8 like terms Add- same signs coefficients only (don’t add exp.) FOIL or use Distributive Property =8x2 - 12x - 16x + 24 =8x2 – 28x + 24

  11. #7) (4x – 2y)(4x – 3y) Distribute the 4x Multiply (don’t forget to add exponents when multiplying) Distribute the -2y like terms add - same signs coefficients only (don’t add exp.) FOIL or use Distributive Property =16x2 - 12xy - 8xy + 6y2 =16x2 – 20xy + 6y2

  12. #8) (2x + 9y)(3x + 2y) Distribute the 2x Multiply (don’t forget to add exponents when multiplying) Distribute the 9y Like terms add-same sign coefficients only (don’t add exp.) FOIL or use Distributive Property =6x2 + 4xy + 27xy + 18y2 =6x2 + 31xy + 18y2

  13. #9) (2x + 5y)(4x - 9y) Distribute the 2x Multiply (don’t forget to add exponents when multiplying) Distribute the 5y like terms subtract- opposite signs coefficients only (don’t add exp.) FOIL or use Distributive Property =8x2 - 18xy + 20xy - 45y2 =8x2 + 2xy - 45y2

  14. 10) (4x - 5y)(5x + 6y) Distribute the 4x Multiply (don’t forget to add exponents when multiplying) Distribute the -5y like terms subtract- opposite signs coefficients only (don’t add exp.) FOIL or use Distributive Property =20x2 + 24xy - 25xy - 30y2 =20x2 - xy - 30y2

  15. 11) (x - 8)(x - 8) Distribute the x Multiply (don’t forget to add exponents when multiplying) Distribute the -8 like terms Add- same signs coefficients only (don’t add exp.) (x-8)2 = (x-8) (x-8) Write it twice!!!!!!!! =x2 - 8x - 8x + 64 =x2 – 16x + 64

  16. 12) (x + 2)(x + 2) Distribute the x Multiply (don’t forget to add exponents when multiplying) Distribute the 2 like terms Add- same signs coefficients only (don’t add exp.) (x+2)2 = (x+2) (x+2) Write it twice!!!!!!!! = x2 + 2x + 2x + 4 = x2 + 4x + 4

  17. (3x2+ ½ ) (3x2+ ½ ) Distribute the 3x2 Multiply (don’t forget to add exponents when multiplying) Distribute the ½ like terms Add- same signs coefficients only (don’t add exp.) (3x2+ ½ )2 = Write it twice!!!!!!!! = 9x4

  18. (2x2 - ¼ ) (2x2 - ¼ ) Distribute the 2x2 Multiply (don’t forget to add exponents when multiplying) Distribute the ¼ like terms Add- same signs coefficients only (don’t add exp.) 14) (2x2 – ¼ )2 Write it twice!!!!!!!! = 4x4

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