Name: Brian

Who is asking: Student
Level: Secondary

Question:
It's about (a+b)x. I remember there a triangle with numbers to remember for a faster solution. Can you please teach me? Thank you.



Hi Brian,

It's called Pascal's Triangle. The first few rows are below. The first row is 1, and the second row is 1 1. Each successive row starts and ends with a 1 and for each other position the number is "the sum of the two numbers above it". For example in the 4th row the first 3 (the one I shaded) is the sum of the shaded 1 and 2 in the row above.

    1     
   1  1   
  1 2  1  
 1 3  3 1 
1 4 6  4 1
.........
The 6th row is then 1   5   10   10   5   1

The numbers in the triangle are called the binomial coefficients. As you suggested they are the coefficients in the expansion of

(a + b) x for x a positive integer. For example (a + b) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3

(the coefficients are 1   3   3   1) and (a + b) 4 = a 4 + 4 a 3 b + 6 a 2 b 2 + 4 a b 3 + b 4

Cheers,
Penny
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