Question

Please help me out with this :)

Answer 1

81
`x^(4)` + 216x³ + 216x² +96x + 16

Explanation:

Using the binomial theorem

With coefficients from Pascal's triangle for n = 4

1 4 6 4 1

with decreasing powers of 3x from
`(3x)^(4)` to
`(3x)^(0\\)`

and increasing powers of 2 from
`(2)^(0)` to
`(2)^(4)`

Thus

`(3x+2)^(4)`

= 1
`(3x)^(4)`
`(2)^(0)` + 4
`(3x)^(3)`
`(2)^(1)` + 6(3x)²(2)² + 4
`(3x)^(1)`
`(2)^(3)` + 1
`(3x)^(0)`
`(2)^(4)`

=1.
`81x^(4)`.1 + 4.27x³.2 + 6.9x².4 + 4.3x.8 + 1.1.16

= 81
`x^(4)` + 216x³ + 216x²+ 96x + 16