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Year 8 Maths Chapter 1 - Algebraic techniques 2 and indices

You will want to refer to Year 7 Maths Chapter 8 for basic algebra skills. This section is more advanced, and omits algebraic language, basic operations, substitution, and other basic concepts.

You will want to refer to Year 9 Maths Chapter 8 for more advanced skills. This section is more basic, and omits FOIL, difference of two squares, perfect squares, and more advanced concepts.

Expanding brackets allows you to look at an equation in a different way. To expand brackets, use the distributive law.

a(b + c) = a × b + a × c
= ab + ac

a(b + c) = a × b - a × c
= ab - ac

You can express this using visual representation.

Illustration of distributive property with rectangles.svg

To the contrary, you can factorise expressions to make them shorter.

Firstly, find the highest common factor (HCF), and then place that outside the brackets. Dividing each term by it, leaving the results in brackets, while using the appropriate operation.

For example, 10x + 15y has a HCF of 5, thus, in it’s factorised form, would be 5(2x + 3y).

Index notation is a convenient method of describing repeated notation. For example 165 is equal to 16 x 16 x 16 x 16 x 16 where 16 is the base and 5 is the index or exponent.

The index law for multiplying expressions which both have indexes is easy.

xm x xn = xm+n. 
xm / xn = xm-n. 

A number raised to the power of 0 is always one. Therefore, a^0 = 1, where a is any real number.

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