Answer:
The coefficient is 144.
Step-by-step 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.
