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# Simplify The Subtract Expression

Sep 17, 2022

### 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) ft

Area of the pool and tiled border:

20 × (2x +20) ft

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

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