Bionomial Expansions C2 help

In class we moved onto binomial expansions and we learnt how to write expansions so for example: (x+y)^4. The teacher gives us homework and i'm fine up until the question asks: Find the coefficient of x^3 in the expansion of: (4+x)^4. I'm very stuck, please help!

The 4th row is 1,4,6,4,1

my bad! it will be 4x^3 then

There isn't a trick in this

If you know how to expand (x+y)^4 then you can just put y = 4 into this and find out what number is in front of the x^3 term.

(If you know the relevant formula you can write this down easily, but if you're just learning this topic then it's best to do it manually so you can see where the numbers come from!)

But the answer in the book is 16? how?

the 4 in (4+x^4 must times by the 4 from Pascals triangle) 4X4 = 16

But the answer in the book is 16? how?

If you use that same application for the next question which is: find the coefficient of x^3 in (1-x)^5 then it would be -5 but the answer is -10

When you expanded (x+y)^4 you should have had a term that was 4x^3y. So when y = 4 this becomes 16x^3.



The relevant coefficients in this case are 1, 5, 10, 10, 5, 1 - check Pascal's triangle

there is no Y term when you expand it -.-

there is no Y term when you expand it -.-