Analyzing Patterns when Multiplying Polynomials

1 / 7

# Analyzing Patterns when Multiplying Polynomials - PowerPoint PPT Presentation

Analyzing Patterns when Multiplying Polynomials. Carol A. Marinas, Ph.D. Using the Distributive Property. When multiplying terms together, use the distributive property and then simplify. Example: (x + 4) ( x + 3) = x (x + 3) + 4 (x + 3)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Analyzing Patterns when Multiplying Polynomials' - benjamin

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Analyzing Patterns whenMultiplying Polynomials

Carol A. Marinas, Ph.D.

Using the Distributive Property
• When multiplying terms together, use the distributive property and then simplify.
• Example: (x + 4) ( x + 3) =

x (x + 3) + 4 (x + 3)

=(x2 + 3x) + (4x + 12) = x2 + 7x + 12

Example:

(x + 2) (x - 2) =

x (x - 2) + 2 (x- 2)=

(x2-2x) + (2x - 4)

= x2 - 4

Pattern:

(a - b) ( a + b)

OR

(a + b) ( a - b)

= a2 - b2

Pattern Recognition:Sum and Difference of the same 2 terms
Example

( x + 3 ) 2 =

(x + 3) (x + 3) =

x(x + 3) + 3(x + 3) =

(x2 + 3x) + (3x + 9)=

x2 + 6x + 9

Pattern

(x + a) 2 =

x2 + 2 ax + a2

Note : ( x - 3)2 = x2 - 6x + 9

Because a = -3 so x2 + 2(-3)x + 9

Pattern Recognition:Square of a Binomial
Example:

(x + 2) ( x + 5) =

x(x + 5) + 2 (x+ 5) =

(x2 + 5x) + (2x + 10) =

x2 + 7x + 10

Pattern:

(x + a) ( x + b) =

x2 + (a+b)x + ab

Note:

(x - 3) (x + 5) =

x2 + 2x - 15 because a = -3 and b = 5. So a+b = 2 and ab = -15.

Pattern Recognition:Form (x + a) (x + b)
Example:

(x +3) (x2 -3x + 9)=

x (x2 -3x + 9) +

3 (x2 -3x + 9)=

x3- 3x2 + 9x +

3x2 - 9x + 27=

x3 + 27

Pattern:

(x + a) (x2 -ax + a2) = x3 + a3

OR

(x - a) (x2 + ax + a2) = x3 - a3

Pattern RecognitionForm (x + a)(x2 - ax + a2)
Hope this helps ...