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

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

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Graph 4 ≤ x ≤14 2 4 6 8 10 12 14 16 18 N o w s h a d e B e t w e e n t h e c i r c l e s ! ! What kind of Circles?

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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? 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 % (2,000)(R)(4)

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FOIL or use Distributive Property 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.)

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FOIL or use Distributive Property #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.)

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FOIL or use Distributive Property #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.) =12x 2 - 32x +15x- 40 =12x 2 – 17x - 40

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FOIL or use Distributive Property #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.) =15x 2 - 10x- 6 =15x 2 – 1x - 6 +9x

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FOIL or use Distributive Property #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.) =6x 2 - 21x - 4x+ 14 =6x 2 – 25x + 14

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FOIL or use Distributive Property #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.) =8x 2 - 12x - 16x+ 24 =8x 2 – 28x + 24

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FOIL or use Distributive Property #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.) =16x 2 - 12xy - 8xy+ 6y 2 =16x 2 – 20xy + 6y 2

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FOIL or use Distributive Property #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.) =6x 2 + 4xy + 27xy + 18y 2 =6x 2 + 31xy + 18y 2

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FOIL or use Distributive Property #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.) =8x 2 - 18xy + 20xy - 45y 2 =8x 2 + 2xy - 45y 2

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FOIL or use Distributive Property 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.) =20x 2 + 24xy - 25xy- 30y 2 =20x 2 - xy - 30y 2

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(x-8) 2 = 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 2 - 8x + 64 =x 2 – 16x + 64 Write it twice!!!!!!!! (x-8)

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(x+2) 2 = 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 + 2x + 4 = x 2 + 4x + 4 Write it twice!!!!!!!! (x+2)

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(3x 2 + ½ ) 2 = (3x 2 + ½ ) (3x 2 + ½ ) Distribute the 3x 2 Multiply (don’t forget to add exponents when multiplying) Distribute the ½ like terms Add- same signs coefficients only (don’t add exp.) = 9x 4 Write it twice!!!!!!!!

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

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© 2012 National Heart Foundation of Australia. Slide 2.

© 2012 National Heart Foundation of Australia. Slide 2.

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