Addition and Subtraction of Linear Algebraic Expressions
An algebraic expression can be simplified by:
"grouping" of the same variables and number operations.
Example
Simplify 2a + 4 + 2a + 1
= 2a + 4a + 4 + 1 (Step 1 : "Group" variables and numbers)
= 6a + 5 (Step 2 : Do the + - )
Example
Do the followings:
a. 4a + 2b + 5a + b
= 4a + 5a + 2b + b (Step 1 : Group same variables together)
= 9a + 3b (Step 2 : Do the + - )
b. 8p - 4q - 2p +5q (Step 1 : Group same variables together)
= 8p + 2p - 4q + 5q (Step 2 : Do the + - )
= 10p + q
Simplify Linear Algebraic Expressions
Use of Bracket and Order of Operations
Property: a ( b + c) = ab + ac
3 ( a + b ) = 3 x ( a + b ) = ( a + b ) x 3 preferred written form is 3(x + y)
½ ( u + v ) = (u + v) = ½ u + ½ v
2
Example
Simplify 5y – 2(y – 2)
= 5y – 2y - 2 x -2 (Step1 : Open Bracket)
= 3y – 4 Step2: Do x / + -)
Example
Simplify 7y – 2(3y – 5)
= 7y – 6y + 10
= y + 10
Example
Simplify -2(3p - 5) + 4p
= -2 x 3p -2 x -5 + 4p (Step1 : Open Bracket)
= -6p + 10 + 4p (Step2: Do x / + -)
= 10 - 2p
Practice
1. Do the followings:
a. 5a + 2 + 6a - 1
b. 9a - 6b + a - 2b
c. 4a + 2a - 4a
d. 1 + a - 1 + b
2. Simplify the followings:
a. 3y + (2 - y)
b. 5(a + b) - 2a
c. 4p - (p - 1)
d. 2(p + q + 1) - 1/2
e. 3/4 (a + b) - 1/3(a + 2b)
