Using The Formula

Using The Formula; n=positive integer

MathsDirect

Reminder, the binomial formula is

Find the first 4 terms of the expansion of

Note 3!=6

When you have more complicated terms inside the brackets, you must be very careful about how you write the first line of working.

Find the first 4 terms of the expansion

The minus sign in the bracket, will mean that the sign of each term will alternate

You may be asked to find all the terms, up to a certain power of x. You must be quite sure that you have fulfilled the requirement before you stop.

Find, up to the power of x³ the expansion of

Obviously, any further terms would be above x³.

You will need to be a bit more careful if powers or fractions are included in the brackets.

Expand, up to powers of x⁵

The last term is too high for our range.

So the answer to the question is

One application of the binomial theorem, is easily approximating expressions like (0.98)¹⁰, which will be demonstrated on the next page.