removing parentheses

Parentheses bundle a group of terms together; removing them unties the bundle so the inner terms can mix with the rest of the expression. The catch is the sign sitting just in front of the bundle — it decides what happens to each term as it comes out.

There are two cases. A plus (or nothing) before the parentheses leaves the inner terms unchanged: +(a - b) becomes a - b. A minus before the parentheses flips the sign of every inner term: -(a - b) becomes -a + b. If a number multiplies the parentheses, you distribute it to every term: 3(a - b) becomes 3a - 3b. The minus case is really just multiplying by -1.

The single most common error is flipping only the first term after a minus sign and forgetting the rest. Every term inside must respond to the sign in front — change all of them, or none of them. Once the parentheses are gone, you can combine like terms across the whole expression.