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
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
Simplify algebraic expression with Fractions
- Simplify fractional linear expression with common denominator into a single fraction
Example:
Simplify y + (y + 2)
2 3
Step 1 : Multiply each for same denominator (L.C.M)
L.C.M : 3 , 2 = 6
= y x3 + (y + 2)
2 x3 3x2
Step2: Combine the fractions into a single fraction
= 3y + (2y + 2)
6 6
= 3y + 2y + 2
4y
= 5y + 2
4y
Example
Simplify 5y - 3(y + 1)
3 2
= 2x5y – 3x3(y + 1) (Step 1 : Multiply each for same denominator (L.C.M))
2x 3 3x 2
= 10y – 9(y + 1) (Step2 : Combine the fractions into a single fraction)
6 6
= 10y – (9y + 1)
6
= 10y – 9y – 9 (Step 3 : Simplify : Do Order of Operations)
6
= y – 9
6
Example:
Simplify 4y + 3(y-1)
3 2
=2 x 4y + 3x3(y-1) (Step 1 : Multiply each for same denominator (L.C.M))
6 6
= 8y +9y – 9 (Step2 : Combine the fractions into a single fraction)
6 (Step 3 : Simplify : Do Order of Operations)
= 17y – 9
6
Example
Simplify 2q - 3(q - 5)
3 2
= 2 x q - 3 x 3(q - 5) (Step1 : Multiply each to get the same denominator)
2 x 3 3 x 2
= 2q -9(q - 5) (Step2 : Simplify and Do Order of Operations)
6 6
= 2q - 9q + 45
6
= -7q +45
6
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)
3. Simplify 2x - 3(x - 2) [12/I/17/2/A]
3 5
4. Simplify 3x - 2x + 1 [14/II/17/8/A]
2 3
