How do I expand one bracket?

To expand a bracket, you multiply each term inside the bracket by the expression outside the bracket.

Understanding Bracket Expansion

Expanding brackets (also known as parentheses) is a fundamental operation in algebra. It involves removing the brackets by multiplying each term inside the bracket by the term outside. This process simplifies expressions and allows for further calculations.

The Process Explained

Here's a breakdown of how to expand a single bracket:

Identify the expression outside the bracket: This is the term that will be multiplied by each term inside the bracket.
Identify the terms inside the bracket: These are the individual elements separated by addition or subtraction signs within the parentheses.
Multiply each term: Multiply the expression outside the bracket by each term inside the bracket.
Simplify: Combine any like terms to further simplify the expression, if possible.

Example

Let's say we have the expression: 3(m + 7)

According to the provided information, to expand this bracket:

We multiply m by 3, resulting in 3m.
We multiply 7 by 3, resulting in 21.

Therefore, 3(m + 7) = 3m + 21.

General Formula

The general formula for expanding a single bracket is:

a(b + c) = ab + ac

Where:

a is the expression outside the bracket.
b and c are the terms inside the bracket.

Additional Examples

2(x - 4) = 2x - 8
-5(y + 2) = -5y - 10
x(x + 3) = x² + 3x

Tips for Accuracy

Pay attention to signs: Be especially careful with negative signs. Remember that multiplying a positive term by a negative term results in a negative term, and multiplying two negative terms results in a positive term.
Distribute carefully: Make sure to multiply the term outside the bracket by every term inside the bracket.
Double-check your work: It's always a good idea to review your work to catch any potential errors.

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