Question

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

Answer 1

The coefficients of a binomial expansion are determined by the Pascal's triangle.

Take a look at the picture.

draw the Pascal's triangle up to the third row. (the row with only 1 is the zero'th row)

Also, notice that as we expand
`(A+B) ^(3)`,
in each term the power of A decreases by 1, starting from 3, and the powers of B increase by 1, up to 3.

According to these, the second term of
`(A+B) ^(3)` is

`3A^(2)B`,

where A=4x, and B=3y,

substituting A an B:


`3A^(2)B=3(4x)^(2)(3y)=3*16 x^(2) *3y=144 x^(2) y`

Answer: 144