Before we begin, let us first recap on the basic information of algebra...
i) Integer = number (Example: 4a)Variable = the alphabet (Example: 4a)
ii) Index = the small number on the top right hand corner (Example: 4a2 )
iii) Like terms: 3ab + 2ab (Example)Unlike terms: 2a + 3b (Example)

Now, since we have recalled on the different terms in algebra, we shall move on to Algebraic Expansion...
There are a variety of ways to expand the algebraic expressions. I shall only include those that are usually used in examinations.

i) Product of single terms
Example: (ab)(b2c)
- Group the product of b together. Then, express the product in index form.

(ab)(b2c)
= (a x b) x (b x b x c)
= a x (b x b x b) x c
= ab3c

ii) Product of Two Expressions
Example: a(x+y)

a(x + y) = ax + ay

This is called multiplying in the number in front ONE BY ONE into the brackets.The 'a' in the expression is multiplied step by step into the bracketed numbers, first, a x x and a x y, which gives us ax and ay respectively.

To give you a better idea, watch the short clip on Algebraic expansion:



iii) Using the THREE golden rules of Algebraic Expansion
- Saves time
- Easier method

(a + b)2 = (a)2 + 2(a)(b) + (b)2
(a - b)2 = (a)2 - 2(a)(b) + (b)2
(a + b)(a - b) = (a)2 - (b)2

So, just replace the 'a' and the 'b' with the actual numbers or expressions, and then voila! We have the answer!
To have a better understanding, just watch the video, it is actually very useful!



If you have any questions or queries after reading this, feel free to approach me in school or email me at merlion0512@hotmail.com
Thankyou!
And credits to Aravind who spotted some of my typos, kudos! =)

Weishi!

Labels: Mathematics