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Multiply Binomials

This resource covers the multiplication of binomials, explaining techniques such as FOIL and the Distributive Property. It also dives into solving and graphing inequalities, particularly in the context of the statements like |x - 9| ≤ 5. The text provides specific examples, demonstrating how to manipulate terms, identify and graph 'and' statements, and combine like terms. Additionally, the calculation of simple interest is introduced, along with concepts of annual interest rates. Essential for students exploring algebraic structures and inequalities.

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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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