Multiplying Out Brackets

Basics of Brackets

Brackets in algebra are used to group terms together and to set priority of operations.
We multiply out brackets to simplify expressions, making them easier to understand and work with.
The process involves multiplying each term inside the bracket by the term outside the bracket.
This rule is often referred to as the Distributive Law, stated as a(b + c) = ab + ac.

Single brackets multiplication: When an expression consists of a single bracket, multiply the factor outside the bracket with each term inside the bracket. For example, 2(3x + 5) = 6x + 10.
Square of a binomial: Recognise this as a special case where the same bracket is multiplied by itself. It follows the rule (a+b)² = a² + 2ab + b². For instance, (x + 5)² = x² + 10x + 25.
Product of two different binomials: This involves multiplying each term in the first bracket with each term in the second. It follows the rule (a + b)(c + d) = ac + ad + bc + bd. For instance, (x + 2)(x - 3) = x² - 3x + 2x - 6 = x² - x - 6.

Be cautious when dealing with negative numbers. Consider the negative sign as part of the term.
For example, simplifying 3(x - 2) = 3x - 6. The negative sign is considered part of the 2, so keep signs consistent when distributing.

Make sure to multiply each term within the brackets individually, not just the first.
Be careful to keep track of positive and negative signs.
Checking your answer is always a good idea. You can do this by expanding the equation if it were in its original, bracketed form.
Regular practice will help you get proficient at multiplying out brackets.

Remember, the consistent application of these rules will help you simplify complex algebraic expressions, making them easier to work with.