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

Question

asked Jan 23, 2017 45.8k views

2 Answers

Akash Deep · Answer 1 · 2017-01-28T15:30:12+0000

Answer:

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:
if you solve that the result is the general formula. The same for

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.