Expanding using several terms and symbols

When there is a minus sign in front

When the factor in front of the brackets is negative, you must pay particular attention to the signs. The rule remains the same, but each multiplication must take the sign into account.

-k(a+b) = -k×a - k×b

Example

Expand -3(x-2):

• -3 × x = -3x
• -3 × (-2) = +6
• Result: -3x + 6

The special case of -(a+b)

When there is no number in front of the brackets but just a minus sign (-), this is equivalent to multiplying by -1:

-(a+b) = -a - b -(a-b) = -a + b

Example: -(x+7) = -x - 7 and -(2x-5) = -2x + 5

Expanding an expression with more than two terms

The rule applies in the same way even if the parentheses contain three or more terms.

2(x+y-3) = 2×x + 2×y - 2×3 = 2x + 2y - 6

Summary table of signs

Sign of the factor	Sign inside the brackets	Sign of the resulting term
+	+	+
+	-	-
-	+	-
-	-	+

This table corresponds to the rule for signs in multiplication: two identical signs give +, two different signs give -.

Common pitfall

Watch out for double negative signs! In -3(x-2), many pupils forget that -3 multiplied by -2 gives +6 (not -6). Always take the time to apply the sign rule term by term, without rushing.