By: Anna Smoak Multiplying Polynomials. 10 inches7 ’’3’’ 6 inches 3 ’’ How many different ways can you find the area of the large rectangle? Warm Up:

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Presentation transcript:

By: Anna Smoak Multiplying Polynomials

10 inches7 ’’3’’ 6 inches 3 ’’ How many different ways can you find the area of the large rectangle? Warm Up:

10 inches 7 ’’3’’ 6 inches 3 ’’ Method: A=LxW A=10 in x 6 in A=60 in 2 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 in in in in 2 A=60 in 2 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 in in in in 2 A=60 in 2 OR A=7 in(3 in + 3 in) + 3 in(3 in + 3 in) A=21 in in in in 2 A=60 in 2

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

x + 2 2x x + 1 x 1 x2x2 2x x2 But this is the same as distributing (x + 1)(x + 2) = x ( x + 2) + 1 (x + 2) = x 2 + 2x + 1x + 2 = x 2 + 3x + 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) = x 2 + 2x + 1x + 2 = x 2 + 3x + 2 Find: (x + 1)(x + 2)

x x x + 3 x 3 x2x2 2x x2 But this is the same as distributing as well (x + 3)(x - 5) = x (x – 5) + 3 (x – 5) = x 2 - 5x + 3x - 15 = x 2 - 2x - 15 To find the total area we can find the sum of two smaller areas. x(x – 5) + 3 (x – 5)= x 2 – 5x + 3x – 15= x 2 – 2x – 15 Find: (x + 3)(x - 5)

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

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

WORK IN PAIRS Simplify : (2y 2 + 7y – 5)(3y 2 – 5y + 4)

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