Answer:
1215
Step-by-step explanation:
Using the Binomial theorem
With coefficients obtained from Pascal's triangle for n = 6, that is
1 6 15 20 15 6 1
and the term 3x decreasing from [tex](3x)^{6}[/tex] to [tex](3x)^{0}[/tex]
and the term - y increasing from ([tex](-y)^{0}[/tex] to [tex](- y)^{6}[/tex]
Thus
[tex](3x-y)^{6}[/tex]
= 1 × [tex](3x)^{6}[/tex] [tex](-y)^{0}[/tex] + 6 × [tex](3x)^{5}[/tex] [tex](-y)^{1}[/tex] + 15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex] + .........
The term required is
15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex]
= 15 × 81[tex]x^{4}[/tex] y²
with coefficient 15 × 81 = 1215
that is 1215[tex]x^{4}[/tex]y²