Multiplying polynomials
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Multiplying Polynomials. How Do you find the area of a rectangle? . How would you find the area of this house lot?. x ² . 2x. 5x. 10. x ² + 2x + 5x + 10 = x ² + 7x + 10. Find The Area of the Lot. 3x. 5. 2x. 6x ² . 10x. 8. 24x. 40. 6x ² + 24x + 10x + 40 =

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How do you find the area of a rectangle
How Do you find the area of a rectangle?

  • How would you find the area of this house lot?

2x

5x

10

x² + 2x + 5x + 10 =

x² + 7x + 10


Find the area of the lot
Find The Area of the Lot.

3x

5

2x

6x²

10x

8

24x

40

6x² + 24x + 10x + 40 =

6x² + 34x + 40


Example 1 find the product of 3x 5 5x 10
Example 1: Find the product of (3x + 5) (5x – 10)

3x

+5

5x

25x

15x²

-10

-30x

-50

15x² - 30x + 25x - 50 =

15x² - 5x - 50


3x 5 5x 10 using the foil method only used when multiplying 2 binomials
(3x + 5) (5x – 10) Using The FoIL Method*only used when multiplying 2 binomials

F – First

O- Outer

I – Inner

L - Last


3x 5 5x 10
(3x + 5) (5x – 10)

  • First: first number times the first number

    (3x +5) (5x–10)

    3x(5x)

    = 15x²

  • Outer: Outer number times the outer number

    (3x +5) (5x–10)

    3x(–10)

    = -30x


3x 5 5x 101
(3x + 5) (5x – 10)

  • Inner: inner number times the inner number

    (3x +5) (5x–10)

    5(5x)

    = 25x

  • Last: Last number times the last number

    (3x +5) (5x–10)

    5(–10)

    = -50


  • F: 15x²

  • O: -30x

  • I : 25x

  • L: -50

    15x²- 30x + 25x - 50 =

    15x² - 5x - 50


Example 2 find the product of 4x 9 x 11
Example 2: Find the Product of (4x – 9)(x – 11)

= 4x² -53x +99

Example 3: Find the Product of (5x – 4)(5x + 4)

= 25x² - 16

Example 4: Find the Product of (3x + 9)(3x +9)

= 9x² + 54x + 81


Example 5 find the product of 2x 2x 12 5x 1
Example 5: Find the Product of (2x² – 2x + 12)(-5x – 1)

-5x

-1

2x²

-10x³

-2x²

10x²

2x

-2x

-60x

12

-12

= -10x³

+8x²

-58x

-12


2x 2x 12 5x 1
(2x² – 2x + 12)(-5x – 1)

2x²(-5x) +

2x²(-1)

-2x(-5x)

-2x(-1)

+12(-5x)

+12(-1)

= -10x³

-2x²

+10x²

+ 2x

-60x

-12

= -10x³

+ 8x²

- 58x

- 12


Find the product of a xy b x y c x y d x y x y
Find the product of:A) (xy)²b) (x + y)²c) (x – y) ²d) (X +y) (x – y)

=x²y²

=x² + 2xy +y²

=x² - 2xy +y²

=x² - y²


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