Answer:
[tex]\sf 81x^4+216x^3+216x^2+96x+16[/tex]
Step-by-step explanation:
Binomial Theorem
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
Factorial is denoted by an exclamation mark "!" placed after the number.
It means to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
Given function:
[tex]\sf f(x)=(3x+2)^4[/tex]
Compare with the Binomial Theorem:
Substitute the values into the Binomial Theorem formula:
[tex]\begin{aligned}\sf (3x+2)^4 & = \sf (3x)^4+\dfrac{4!}{1!3!}(3x)^3(2)+\dfrac{4!}{2!2!}(3x)^2(2^2)+\dfrac{4!}{3!1!}(3x)^1(2^3)+2^4\\\\& = \sf 81x^4+4(27x^3)(2)+6(9x^2)(4)+4(3x)(8)+16\\\\ & = \sf 81x^4+216x^3+216x^2+96x+16 \end{aligned}[/tex]
Learn more about binomial expansion here:
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