Properties for simplifying algebraic expressions

This lesson gives you a list of nine important properties for simplifying algebraic expressions.

Let a,b,and c represent real numbers.

Definition of subtraction :  a - b = a + (-b)

Definition of division : a ÷ b = a/b = a × 1/b, b ≠ 0

Multiplication by zero : 0 × a = 0

Multiplication by -1 : -1 × a = -a

Distributive property for subtraction : a(b - c) = ab - ac 

Opposite of a difference : -(a - b) = b - a

Opposite of a sum : -(a + b) = -a + -b

Opposite of a product : -(ab) = -a × b =  a × -b

Opposite of an opposite : -(-a) = a

Using the properties for simplifying algebraic expressions


Match the equation with the appropriate property name

A. 4(x - y) = 4x - 4y                           

B. (x - 2) ÷ 5z = (x - 2) / 5z                 

C. -(t-1) = -1(t-1)                               

D. 2d - 7 = 2d + (-7) 

E. -( 2d - 7) = 7 - 2d

F. -[-(8 + s)] = 8 + s

G. -(12xy) = 12(-xy)

H. -[3 + (-a)] = -3 + [-(-a)]

I. (10x2 - 15y)(0) + -x = 0 + -x 

1. Definition of division

2. Opposite of a sum

3. Opposite of an opposite

4. Opposite of a product

5. Multiplication by zero

6. Multiplication by -1

7. Opposite of a difference

8. Distributive property for subtraction

9. Definition of subtraction

Show answer

Recent Articles

  1. What is Velocity? Definition and Examples

    Jun 27, 22 08:45 AM

    Learn the difference between velocity and speed and the meaning of constant velocity.

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.