The document discusses expanding algebraic expressions by removing brackets. It explains that removing brackets, also called expanding, turns expressions like a(b + c) into a*b + a*c by distributing the term outside the brackets. The document provides examples of expanding expressions like 2(a + 1) and 3(x - 2). It also defines a term as a group of numbers and letters, like 4b, 2y, or 3x^2.

1. October 4, 2012
Brackets and factors
1. Brackets
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2. Explanation October 4, 2012
Look at this shape…
2 8
2
You can work out the total area by calculating 2 × (2 + 8)
This is equal to 2 × 2 plus 2 × 8 or 4 + 16
The same is true in algebra
a(b + c) means “add b and c, then multiply by a”.
This is the same as “multiply a by b and multiply a by c,
then add the two results”.
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3. Example October 4, 2012
Multiplying to get rid of the brackets in 2 × (2 + 8)
to make 2 × 2 + 2 × 8 is called expanding.
Once you have got rid of the brackets by expanding,
you can simplify, or group things that are the same.
Remember, there are certain general simplifications…
2×a should be written 2a
a×a should be written a ²
a×b should be written ab
so
2 × (2 + 8) could be expanded as 2² + 16
and a × (a + 8) would be expanded as a² + 8a
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4. Practise October 4, 2012
Expand and simplify as far as you can the following…
2(a + 1) 2a + 2
3( x – 2) 3x – 6
2a (a – 1) 2a² – 2a
2b (a – b ) 2ab – 2b²
2ab(a – b ) 2ba² – 2ab²
2 (2x + y ) + 2 (2x + 2y ) 4x + 2y + 4x + 4y 8x + 6y
A group of numbers and letters, such as 4b, 2y or 3x²
is known as a term.
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