Simplify The Subtract Expression

Key Concepts

• Subtract expressions by using properties
• Subtract expressions with rational coefficients
• Subtract more complex expressions

4.7 Subtract expressions 

• For subtracting two or more algebraic expressions, it requires categorizing the terms in an algebraic expression into two types – like and unlike terms. 
• Then, taking up the like terms and then subtracting them accordingly.  
• The other way is to follow the horizontal method that requires writing the expressions to be subtracted below the expression from which it is to be subtracted.  
• Like terms are placed below each other.  

• The sign of each term that is to be subtracted is reversed, and then the resulting expression is added normally. 

Example: 

4.7.1 Subtract expressions by using properties 

Example 1: 

Lenin wants to put a tiled border around their swimming pool; what expression represents the total area of the border? 

Solution: 

Write an expression for the area of the pool only. 

Then write an expression for the area of the pool plus the tiled border. 

Area of the pool l width × length 

16 × (2x +16) ft²  

Area of the pool and tiled border: 

20 × (2x +20) ft²  

Use properties of operations to subtract the expression 

(Area of the pool + tiles) – (area of the pool) 

=20 (2x +20) – 16(2x +16) 

= 40x – 32x +400 – 256 

=8x +144 

The area of the tiled border is 8x +144 ft².  

Example 2:  

Simplify the expression using the distributive property. 

4(x – 5) – (x + 3) 

Solution: 

4(x – 5) – (x + 3) 

4.7.2 Subtract expressions with rational coefficients 

Coefficient: The number multiplying by a variable.  

Rational: Can be represented by a fraction – both positive and negative numbers included.  

Example1: 

Subtract (0.95x- 0.04) – (0.99x – 0.13) 

Solution: 

(0.95x- 0.04) – (0.99x – 0.13) 

= 0.95x- 0.04 + (-1) (0.99x – 0.13) 

4.7.3 Subtract more complex expressions 

Complex expressions: 

complex expressions are mathematical expressions that include complex numbers, which contain both a real part and an imaginary part. 

Complex numbers look like binomials in that they have two terms.  

For example, 3 + 4i is a complex number as well as a complex expression. 

Example 1:  

Subtract (16+3.4m+8k) – (6.6m – 6 +3k) 

Solution: 

(16+3.4m+8k) – (6.6m – 6 +3k) 

(16+3.4m+8k) + (-6.6m + 6 -3k) 

=16+3.4m+8k -6.6m + 6 -3k 

=8k – 3k +3.4m – 6.6m +16+6 

=5k -3.2m + 22

 

Exercise:

1. Subtract.
   (14x) – (–15 + 7x)
   (4y – 6) – (–y – 3)             
2. Subtract and simplify.
   1/4  m – 2/8 m + 1/2
3. Rewrite the expression 16m –(4+12m) without parentheses.
4. Write an equivalent expression to 6k-(3+2k) without parentheses, then simplify.
5. A rectangular garden has a walkway around it. Find the area of the walkway

6. Find the difference (6x – 3  ) – (–2x +4  )

7. An expression is shown (0.34 – 0.2) – (0.4n – 0. 15)
Create an equivalent expression without parentheses.

8. Subtract (16+3.5t+4s) – (2.4m- 5 +2s).

9. Subtract (0.75a – 0.03) – (0.78a-0.12).

10. A soap company has two manufacturing plants with a daily production level of 7x + 7 and 4x – 2 items, respectively, where x represents a minimum quantity. The first plant produces how many more items daily than the second plant?

Concept Map

What have we learned:

• Understand how to subtract the expressions.
• Understand how to subtract expressions by using properties.
• Subtract expressions with rational coefficients.
• Subtract more complex expressions