Distribute The Negative Calculator

Distributing the negative sign is a fundamental algebraic operation that simplifies expressions by removing parentheses. This calculator helps you perform this operation quickly and accurately.

What is Distribute the Negative?

Distributing the negative sign is the process of multiplying the negative sign by each term inside parentheses. This operation is based on the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.

When dealing with negative numbers, the negative sign is distributed to each term inside the parentheses, changing the sign of each term. For example, -3(4 + 5) becomes -3*4 + (-3)*5 = -12 - 15 = -27.

Formula

-a(b + c) = -ab - ac

-a(b - c) = -ab + ac

How to Distribute the Negative

To distribute the negative sign in a mathematical expression:

Identify the negative sign and the parentheses.
Multiply the negative sign by each term inside the parentheses.
Remove the parentheses.
Simplify the expression by performing the multiplication.

Important Note

Remember that distributing the negative sign changes the sign of each term inside the parentheses. If a term is positive, it becomes negative, and if a term is negative, it becomes positive.

Examples

Let's look at some examples of distributing the negative sign:

Example 1

Expression: -2(3 + 4)

Step 1: Distribute the negative sign: -2*3 + (-2)*4

Step 2: Perform the multiplication: -6 - 8

Final result: -14

Example 2

Expression: -5(6 - 2)

Step 1: Distribute the negative sign: -5*6 + (-5)*(-2)

Step 2: Perform the multiplication: -30 + 10

Final result: -20

Example 3

Expression: -3(x + y)

Step 1: Distribute the negative sign: -3x - 3y

Final result: -3x - 3y

Common Mistakes

When distributing the negative sign, it's easy to make a few common mistakes:

Forgetting to distribute the negative sign to all terms inside the parentheses.
Changing the sign of the negative sign itself, which is not necessary.
Incorrectly applying the distributive property to terms that are not inside parentheses.

Tip

To avoid mistakes, double-check each term inside the parentheses and ensure that the negative sign is distributed correctly to each one.

FAQ

Why is distributing the negative sign important?

Distributing the negative sign is important because it simplifies expressions and makes them easier to work with. It also helps in solving equations and simplifying algebraic expressions.

Can I distribute the negative sign to terms outside the parentheses?

No, the distributive property only applies to terms inside the parentheses. You cannot distribute the negative sign to terms outside the parentheses.

What happens if I forget to distribute the negative sign?

If you forget to distribute the negative sign, you may end up with an incorrect result. For example, -2(3 + 4) would incorrectly become -2*7 = -14 instead of -6 - 8 = -14.

Is there a difference between distributing a negative sign and a positive sign?

Yes, distributing a negative sign changes the sign of each term inside the parentheses, while distributing a positive sign leaves the signs of the terms unchanged.