1. **State the problem:** Expand the expression $ (x+3)^4 $ into a standard polynomial form. 2. **Formula used:** Use the Binomial Theorem which states: $$ (a+b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k $$ where $ \binom{n}{k} $ are binomial coefficients. 3. **Apply the formula:** Here, $a = x$, $b = 3$, and $n = 4$. 4. **Calculate each term:** - For $k=0$: $\binom{4}{0} x^{4} 3^{0} = 1 \cdot x^4 \cdot 1 = x^4$ - For $k=1$: $\binom{4}{1} x^{3} 3^{1} = 4 \cdot x^3 \cdot 3 = 12x^3$ - For $k=2$: $\binom{4}{2} x^{2} 3^{2} = 6 \cdot x^2 \cdot 9 = 54x^2$ - For $k=3$: $\binom{4}{3} x^{1} 3^{3} = 4 \cdot x \cdot 27 = 108x$ - For $k=4$: $\binom{4}{4} x^{0} 3^{4} = 1 \cdot 1 \cdot 81 = 81$ 5. **Combine all terms:** $$ (x+3)^4 = x^4 + 12x^3 + 54x^2 + 108x + 81 $$ 6. **Final answer:** The polynomial in standard form is: $$ x^4 + 12x^3 + 54x^2 + 108x + 81 $$