# DISTRIBUTIVE PROPERTY

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```					                 DISTRIBUTIVE PROPERTY
a(x+ y) = ax + ay
bc + bx = b(c + x)

Multiplying a sum is the same as multiplying each term of the
sum by that factor and then adding the products.

6(3 + 5) = 63 + 65
a(2x + 3) = 2ax + 3a
c(w – 2d) = cw – 2cd
x(2x + y) = 2x2 +xy

The distributive property can also be demonstrated with a
geometric model:
x   + y
a ax   ay
Area of large rectangle = a(x + y)

Sum of area of small rectangles = ax + ay

So then a(x + y) must equal ax + ay

FACTORING:
Going from the form ax + ay to a(x + y) is called factoring
Examples:
3w + 3z can be factored as 3(w + z)
3w + 6z can be factored as 3(w + 2z)
10q + 15x can be factored as 5(2q + 3x)
10xyz + 25x can be factored as 5x(yz + 5)
12abc + 16ab can be factored as 4ab(3c +4)
4x3 + 3x can be factored as x(4x2 + 3)
(Going from the form a(x +y) to ax + ay is called multiplying
through or distributing)

Exponents:
3333 = 34  34 = 81
W  W  W = W3

Prime Factorization:
The prime factorization of a number is when the number is
written as a product of all prime numbers.
15 = 3 5      18 = 2 3  3 42 = 2 3  7 16 = 2 2  2  2
A factor tree can be used to find the prime factorization
30           30 = 2  3  5

5            6

2            3

```
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