Question

I need helpThis is from my ACT Prep guide, in the calculus portion

Answer 1

Given the expression:

`(2x^2y^3+y)^7`

We will find the 4th term using the binomial theorem

the general form of the binomial theorem will be:

`(a+b)^n=^nC^{}_r\cdot a^(n-r)\cdot b^r`

So, n = 7, r = 3, a = 2x²y³, b = y

Substitute into the general form

So, the 4th term will be:

`(7!)/(3!4!)\cdot(2x^2y^3)^4\cdot y^3=35\cdot2^6\cdot x^8\cdot y^(12)\cdot y^3=560x^8y^(15)`

So, the answer will be option 3