Dear Maths Help,
I can't understand what Pascal's Triangle has got to do with multiplying out brackets.
For readers who are not familiar with it, Pascal's Triangle (first five rows) is shown below:
Each number in the table is the sum of the two numbers above it.
Now consider what happens if you expand (multiply out) these brackets:
|(1 + x)0||=||1||(Anything to power 0 is 1)|
|(1 + x)1||=||1 + x|
|(1 + x)2||=||1 + 2x + x2|
|(1 + x)3||=||1 + 3x + 3x2 + x3|
What you will notice is that:
In the expansion of (1 + x)n,
the coefficients of the powers of x follow the same pattern as
the nth row of Pascal's triangle.
You don't have to write out Pascal's triangle to find out how brackets expand.
The rth item (counting from 0) in the nth row of Pascal's triangle is
You may have this button on your calculator. Or Maths Help can show you.