### 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:

- What is the expanded form of the following expressions?

a. 5(4x + 2) b. 2(n + 4) - Use the distributive property to expand the following expression.

a. (4 + b) (-a) b. -3(x + 7) - Simplify the following expressions.

a. 1/2 (6x +10) b. (15x – 3) - Use the distributive property to expand 6(4x – 2y) + 5.
- Use the distributive property to write an expression equivalent to y (- 5 – 6x).
- Fill in blanks to expand the equation.

5(t+4)

= (5) (____) +5(_____)

=_______ + _______ . - Fill in blanks to expand the equation.

8(x+2)

= (8) (____) +8(_____)

=_______ + _______ . - Write the expanded form of the expression 8(y+x).
- Expand (5+4x-3).
- 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

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