# Adding & Subtracting Algebraic Expressions

Only like terms may be added or subtracted. To add or subtract like terms, merely add or subtract their coefficients:

You may add or multiply algebraic expressions in any order. This is called the commutative property:

x + y = y + x |

xy = yx |

For example, â€“2

*x*+ 5*x*= 5*x*+ (â€“2*x*) = (5 â€“ 2)*x*= 3*x*and (*x*â€“*y*)(â€“3) = (â€“3)(*x*â€“*y*) = (â€“3)*x*â€“ (â€“3)*y*= â€“3*x*+ 3*y*.**Caution:**the commutative property does not apply to division or subtraction:

2 = 6 Ã· 3 â‰ 3 Ã· 6 = 1/2

and

â€“1 = 2 â€“ 3 â‰ 3 â€“ 2 = 1.

When adding or multiplying algebraic expressions, you may regroup the terms. This is called the associative property:

x + (y + z) = (x + y) + z |

x(yz) = (xy)z |

Notice in these formulas that the variables have not been moved, only the way they are grouped has changed: on the left side of the formulas the last two variables are grouped together, and on the right side of the formulas the first two variables are grouped together.
For example,

The associative property doesn't apply to division or subtraction:

(

and
*x*â€“ 2*x*) + 5*x*= (*x*+ [â€“2*x*]) + 5*x*=*x*+ (â€“2*x*+ 5*x*) =*x*+ 3*x*= 4*x*2(12

*x*) = (2 x 12)*x*= 24*x*The associative property doesn't apply to division or subtraction:

4 = 8 Ã· 2 = 8 Ã· (4 Ã· 2) â‰ (8 Ã· 4) Ã· 2 = 2 Ã· 2 = 1

and
â€“6 = â€“3 â€“ 3 = (â€“1 â€“ 2) â€“ 3 â‰ â€“1 â€“ (2 â€“ 3) = â€“1 â€“ (â€“1) = â€“1 + 1 = 0.

Notice in the first example that we changed the subtraction into negative addition: (

*x*â€“ 2*x*) = (*x*+ [â€“ 2*x*]). This allowed us to apply the associative property over addition.