Answer:
81[tex]x^{4}[/tex] + 216x³ + 216x² +96x + 16
Step-by-step 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 [tex](3x)^{4}[/tex] to [tex](3x)^{0\\}[/tex]
and increasing powers of 2 from [tex](2)^{0}[/tex] to [tex](2)^{4}[/tex]
Thus
[tex](3x+2)^{4}[/tex]
= 1[tex](3x)^{4}[/tex][tex](2)^{0}[/tex] + 4[tex](3x)^{3}[/tex][tex](2)^{1}[/tex] + 6(3x)²(2)² + 4[tex](3x)^{1}[/tex][tex](2)^{3}[/tex] + 1[tex](3x)^{0}[/tex][tex](2)^{4}[/tex]
=1.[tex]81x^{4}[/tex].1 + 4.27x³.2 + 6.9x².4 + 4.3x.8 + 1.1.16
= 81[tex]x^{4}[/tex] + 216x³ + 216x²+ 96x + 16
