Expand Using Pascal's Triangle (x+4)^4

Pascal\'s Triangle can be displayed as such:

The triangle can be used to calculate the coefficients of the expansion of ${\displaystyle {(a+b)}^n}$ by taking the exponent ${\displaystyle n}$ and adding ${\displaystyle 1}$. The coefficients will correspond with line ${\displaystyle n+1}$ of the triangle. For ${\displaystyle {(x+4)}^4}$, ${\displaystyle n=4}$ so the coefficients of the expansion will correspond with line ${\displaystyle 5}$.

The expansion follows the rule ${\displaystyle {(a+b)}^n=c_0{a}^n{b}^0+c_1{a}^{n-1}{b}^1+c_{n-1}{a}^1{b}^{n-1}+c_n{a}^0{b}^n}$. The values of the coefficients, from the triangle, are ${\displaystyle 1-4-6-4-1}$.

Substitute the actual values of ${\displaystyle a}$ ${\displaystyle x}$ and ${\displaystyle b}$ ${\displaystyle 4}$ into the expression.