The following expressions are equivalent

Explanation

You can show that by simplifying 8(4x), you can reach out to 32x

• Rewrite 4x as 4 • x
  • 8(4x) = 8 • (4 • x)
• Use the associative property of multiplication to group 4 with 8
  • = (8 • 4) • x
• Do the multiplication within the parentheses
  •  = 32x 

We say that 8(4x) = 32x are equivalent expressions because for each of x, they represent the same number.  For example, if x = 10, both expressions have a value of 320.  If x = -3, both expressions have a value of -96.