C4 binomial expansipn help

(1 + 2x)^(1/2) x ( 1 + x )^3

State the set of value of x for which the expansion os valid.

Which bracket do you use?

(1 + 2x)^(1/2) x ( 1 + x )^3

State the set of value of x for which the expansion os valid.

Which bracket do you use?

Hint:

$(1+x)^3 = x^3 + 3x^2 + 3x + 1$

works for all x.

Whichever imposes the greater restriction.

So the one with the smallest power?

In this case yes, but not generally.

What do you mean by imposea thw greatest reatriction?

(1 + 2x)^(1/2) x ( 1 + x )^3

State the set of value of x for which the expansion os valid.

Which bracket do you use?

What do you mean by imposea thw greatest reatriction?

Haha these answers are all unnecessarily complicated and irrelevant , I doubt they've helped you at all

The answer you're looking for is: the one with the smaller range

What do you mean by smallest range?

the one which stops the binomial increasing further, basically if you bionomial expand (1+x) you will only get 1+x, where as (1+x)^3 can expand further so you take the restriction of the first one because its has the smallest range of value possible.

Do you know how to find out the range of x for which a bracket is valid??
If you do, find out what it is for the first bracket, then find it out for the second one, and whichever range is smallest is the one valid for the whole equation.
If you don't... Well you should, have a read of your notes I guess