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Analyzing Patterns when Multiplying Polynomials - PowerPoint PPT Presentation


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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)

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using the distributive property
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

pattern recognition sum and difference of the same 2 terms
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
pattern recognition square of a binomial
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
pattern recognition form x a x b
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)
pattern recognition form x a x 2 ax a 2
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
Hope this helps ...

To Make Your Multiplying Easier