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Multiplying Polynomials

Multiplying Polynomials. By: Anna Smoak. Warm Up:. 10 inches. 3’’. 7 ’’. 3 ’’. 6 inches. 3 ’’. How many different ways can you find the area of the large rectangle?. Method: A= LxW A=10 in x 6 in A=60 in 2. 10 inches. 3’’. 7 ’’. Method:

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Multiplying Polynomials

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  1. Multiplying Polynomials By: Anna Smoak

  2. Warm Up: 10 inches 3’’ 7 ’’ 3 ’’ 6 inches 3 ’’ How many different ways can you find the area of the large rectangle?

  3. Method: A=LxW A=10 in x 6 in A=60 in2 10 inches 3’’ 7 ’’ Method: Area of large rectangle=The sum of the area of two smaller rectangles A=3 in(3 in +7 in) + 3 in(3 in +7 in) A=9 in2 + 21 in2 + 9 in2 + 21 in2 A=60 in2 OR A=7 in(3 in + 3 in) + 3 in(3 in + 3 in) A=21 in2 + 21 in2 + 9 in2 + 9 in2 A=60 in2 3 ’’ 6 inches 3 ’’ Method: Area of large rectangle=The sum of the area of all the smaller triangles A=(3 in)(3 in)+(3 in)(7 in) + (3 in)(3 in) + (3 in)(7in) A=9 in2 + 21 in2 + 9 in2 + 21 in2 A=60 in2

  4. x + 2 x 2 x x + 1 1 How many different ways can you find the area of the large rectangle?

  5. Find: (x + 1)(x + 2) To find the total area we can find the sum of the smaller areas. (x + 1)(x + 2) = (x)(x) + (x)(2) + (1)(x) + (1)(2) = x2 + 2x + 1x + 2 = x2 + 3x + 2 x + 2 x 2 x2 2x x 2 x x + 1 But this is the same as distributing (x + 1)(x + 2) = x ( x + 2) + 1 (x + 2) = x2+ 2x + 1x + 2 = x2 + 3x + 2 1

  6. Find: (x + 3)(x - 5) To find the total area we can find the sum of two smaller areas. x(x – 5) + 3 (x – 5)= x2 – 5x + 3x – 15= x2 – 2x – 15 x - 5 x -5 x2 2x x But this is the same as distributing as well (x + 3)(x - 5) = x (x – 5) + 3 (x – 5) = x2- 5x + 3x - 15 = x2 - 2x - 15 x + 3 x 2 3

  7. Simplify (x + 3)(x – 2) (Using the distributive property) • x(x - 2) + 3 (x - 2) Distribute the first binomial to the second • x2 - 2x + 3x - 6 Use the distributive property to multiply • x2 + x - 6 Add the like terms

  8. WORK IN PAIRS • How would you simplify the expression (3x + 4)(5x2 – 4x + 6)? Distribute the binomial to the trinomial • 3x(5x2 – 4x + 6) + 4 (5x2 – 4x + 6) = Use the distributive property to multiply • 15x3 – 12x2 + 18x + 20x2 – 16x + 24 = Add the like terms • 15x3 + 8x2 + 2x + 24

  9. WORK IN PAIRS • Simplify : (2y2 + 7y – 5)(3y2 – 5y + 4)

  10. TICKET OUT OF THE DOOR • Find the area of a triangle with base 2x + 3 and height 3x – 1.

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