expand (x+4)^3 — step-by-step solution

Let's expand:

{(x + 4)}^{3}

Using the Newton formula:

{(a + b)}^{n} = \sum_{k = 0}^{n} (\binom{n!}{k! (n - k)!}) a^{n - k} b^{k}

, you can expand the math expression:

\frac{3!}{3! \cdot 0!} \cdot x^{3} \cdot 4^{0}

+ \frac{3!}{2! \cdot 1!} \cdot x^{2} \cdot 4^{1}

+ \frac{3!}{1! \cdot 2!} \cdot x^{1} \cdot 4^{2}

+ \frac{3!}{0! \cdot 3!} \cdot x^{0} \cdot 4^{3}

\frac{3!}{3! \cdot 0!} \cdot x^{3}

+ \frac{6}{2} \cdot x^{2} \cdot 4

+ \frac{6}{2} \cdot x \cdot 16

+ \frac{3!}{0! \cdot 3!} \cdot 4^{3}

\frac{6}{6} \cdot x^{3}

+ 6 \cdot 2 \cdot x^{2}

+ 6 \cdot 8 \cdot x

+ \frac{6}{6} \cdot 64

▷Answer: $x^{3}$ $+ 12 x^{2}$ $+ 48 x$ $+ 64$