Answer:
The coefficient is 144.
Step-by-step explanation:
We have the binomial: [tex](4x+3y)^3[/tex]
The general formula for cubic binomials is:
[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\(a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]
Observation: [tex](a+b)^3=(a+b)(a+b)(a+b)[/tex] if you solve that the result is the general formula. The same for [tex](a-b)^3=(a-b)(a-b)(a-b)[/tex]
Then we have:
[tex](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[/tex]
The coefficient is the number before the variable, then the coefficient of the second term in the expansion of the binomial [tex](4x+3y)^3[/tex] is 144.
