Concept of Expand Expression with Numerical

Key Concepts

• Expand expressions using the distributive property
• Expand expressions with a variable
• Expand more complex expressions

4.4 Expand expressions 

How to expand the expressions? 

Expanding means enlarging something.  

In this case, it means getting rid of any sign of grouping in an expression. Signs of grouping are brackets, parentheses, and braces or curly braces. 

Example: 

Expand: 4 (x + 2). 

Solution: 

Multiply every term inside the brackets by the term outside: 

4.4.1 Expand expressions using the distributive property 

Distributive property:  

The distributive property tells us how to solve expressions in the form of a (b + c).  

The distributive property is sometimes called the distributive law of multiplication and division.  

Then we need to remember to multiply first before doing the addition! 

Example1: 

What is the expanded form of the expression 3.6(t+5)? 

Solution: 

3.6(t+5) 

Example 2: 

What is the expanded form of the expression 4(a+6)? 

Solution: 

4(a+6) 

4.4.2 Expand expressions with a variable 

Variable: An alphabetic character representing a number that is arbitrary or unknown. 

Example 1: 

Use the distributive property to expand the expression x (5- 3.5y) 

Solution: 

x (5- 3.5y) 

Example 2: 

Use the distributive property to expand the expression x (6+ 1.4x) 

Solution: 

x (6+ 1.4x) 

4.4.3 Expand more complex expressions 

Example 1: 

Simplify the expression – 1/4(4 – 10m + 4)  

Solution: 

One way: 

Another way: 

=-1/4(4-10m+4) 

=-1/4(8-10m)  

=(-1/4.  8) +(-1/4 . – 10m) 

=-2+5/2m

Exercise:

1. What is the expanded form of the following expressions?
   a.  5(4x + 2)                          b.  2(n + 4)
2. Use the distributive property to expand the following expression.
   a.   (4 + b) (-a)                      b.  -3(x + 7)
3. Simplify the following expressions.
   a.   1/2 (6x +10)                    b.   (15x  – 3)
4. Use the distributive property to expand 6(4x – 2y) + 5.
5. Use the distributive property to write an expression equivalent to y (- 5 – 6x).
6. Fill in blanks to expand the equation.
   5(t+4)
   = (5) (____) +5(_____)
   =_______  + _______ .
7. Fill in blanks to expand the equation.
   8(x+2)
   = (8) (____) +8(_____)
   =_______  + _______ .
8. Write the expanded form of the expression 8(y+x).
9. Expand (5+4x-3).
10. Select all the expressions equivalent to 16x + 36.
    a.  16(x+20)                           b.  x (16+36)
    c.  4(4x+9)                              d.  2(8x+18).

Concept Map

What have we learned:

• Expand expressions using distributive property.
• Identify variables.
• Expand expressions with a variable.
• How to expand more complex expressions