# How do you use the binomial theorem to expand and simplify the expression #3(x+1)^5-4(x+1)^3#?

##### 1 Answer

The result is

Details of the expansions follow...

#### Explanation:

The first binomial will expand into

The trick is coming up with

Either way, the coefficients turn out to be 1, 5, 10, 10, 5, 1 in that order.

Now multiply the whole thing by 3.

Subtract from this the second expanded binomial (also get the coefficients in one of the ways mentioned above):

The finished result is found by combining like terms (those in #x^3, x^2, x, etc.)

Hope that all makes sense!