Question

Expand the binomial (4x + 3y)3. The coefficient of the second term in the expansion of the binomial (4x + 3y)3

Answer 1

The answer is, 12x +9y

Answer 2

The coefficient is 144.

Explanation:

We have the binomial:
`(4x+3y)^3`

The general formula for cubic binomials is:

`(a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\(a-b)^3=a^3-3a^2b+3ab^2-b^3`

Observation:
`(a+b)^3=(a+b)(a+b)(a+b)` if you solve that the result is the general formula. The same for
`(a-b)^3=(a-b)(a-b)(a-b)`

Then we have:

`(4x+3y)^3=(4x)^3+3(4x)^2.(3y)+3(4x).(3y)^2+(3y)^3\\\\=64x^3+3.16x^2.3y+3.4x.9y^2+27y^3\\\\=64x^3+144x^2y+108xy^2+27y^3`

The coefficient is the number before the variable, then the coefficient of the second term in the expansion of the binomial
`(4x+3y)^3` is 144.