Multiplying Out Brackets

I. Understanding Basics:

Begin with an understanding of what a bracket, also known as a parenthesis, is in algebra. Represented by symbols [ ], { }, ( ), brackets are used to group terms in an equation.
Remember the order of operations in maths - BIDMAS/BODMAS: Brackets, Indices/Orders (power and square roots, etc.), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right)

II. Multiplying Single Terms:

When multiplying within brackets, you follow the same general multiplication rules. For example, 2(3+5) would become 23 + 2*5 = 6 + 10 = 16.

III. Multiplying Multiple Terms:

If the equation includes brackets with more than one term, you need to use the distributive property. Essentially, you distribute the number outside the brackets to every term inside. For example, 2(x+3) would become 2x + 2*3, which simplifies to 2x + 6.

IV. Double Brackets (FOIL Method):

Also known as the ‘First, Outer, Inner, Last’ (FOIL) method, this is used when you have two sets of brackets, e.g., (2x+3)(x-5). Here are the steps: • Multiply the ‘First’ terms in each bracket: (2x * x) = 2x^2 • Then the ‘Outer’ terms: (2x * -5) = -10x • Follow with the ‘Inner’ terms: (3 * x) = 3x • And finally the ‘Last’ terms: (3 * -5) = -15 The result would be 2x^2 - 10x + 3x - 15. Simplify to get: 2x^2 - 7x - 15.

V. Practice and Review:

Continually practise multiplication of brackets as it is fundamental to simplifying and solving algebraic equations. Understanding the concept well will make more complex problems simpler to tackle.
Always review your answers to ensure correct application of multiplication rules and the FOIL method.

Remember, maths is all about understanding the principles and regular practise. The more you engage with these concepts, the better your grasp of algebra will become.