Algebra Period 3 (Monday)

Using the Distributive Property 2-7
Hanging out with an old friend:
THE DISTRIBUTIVE PROPERTY WITH NEGATIVES
The distributive property works the same when there is subtraction in the ( )
a(b - c) = ab - ac

Inverse of a Sum 2-8
Property of -1:
For any rational number a,
(-1) a = -a
In words: MULTIPLYING BY -1 changes a term to its OPPOSITE SIGN

INVERSE OF A SUM PROPERTY:
DISTRIBUTING THE NEGATIVE SIGN
incognito, it's simply distributing -1
TO EACH ADDEND INSIDE THE PARENTHESES

EXAMPLE: -(3 + x) = -1(3 + x) = (-1)(3) + (-1)(x) = -3 + -x or -3 - x
ALL THAT HAPPENED WAS THAT EACH SIGN CHANGED TO ITS OPPOSITE!
-(a + b) = -a - b

Of course they get MUCH HARDER (but the principle is the same!)
[5(x + 2) - 3y] - [3(y + 2) - 7(x - 3)]

Distribute and simplify inside each [ ] first
[5x + 10 - 3y] - [3y + 6 - 7x + 21]

Now, the subtraction sign between them is really a -1 being distributed!
"Double check" to see this (change the subtraction to adding a negative):
[5x + 10 - 3y] + - 1[3y + 6 - 7x + 21]

Distribute the -1 to all the terms in the 2nd [ ]
[5x + 10 - 3y] + -3y + -6 + 7x + - 21

Simplify by combining like terms:
12x - 6y -17