# 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: 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.

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