January 2005
As the question is in the form (a + b)n, we can see that the b part (3x) has to be
raised to the power of 3 - as in the question we need to find the coefficient of x3.
(3x)3
Next we're going to look at what we have to do to the a part. Look at the formula - the a part and the b part's powers
always add up to the power in the question (5), so it has to be 2.
(2)2(3x)3
Now all we need to put in is the nCr value at the beginning. Look at the formula - the r bit is always
the same number as the power b is raised to.
(5C3)(2)2(3x)3
As this is C1 and we can't use calculators, we'll use Pascal's triangle to work it out.
We can see that the third value is 10, so this is what we'll put in the equation.
(10)(2)2(3x)3
All we need to do now is work it out.
10 × 4 × 27x3
1080x3
The coefficient of x3 is 1080.