Question

find the product. (2m + n)^3 = \square

Explanation:

Step1: Recall binomial cube formula

The formula for \((a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\)

Step2: Substitute \(a=2m\), \(b=n\)

$$(2m)^3 + 3(2m)^2n + 3(2m)n^2 + n^3$$

Step3: Simplify each term

$$\begin{align*} (2m)^3 &= 8m^3 \\ 3(2m)^2n &= 3(4m^2)n = 12m^2n \\ 3(2m)n^2 &= 6mn^2 \\ n^3 &= n^3 \end{align*}$$

Step4: Combine all simplified terms

$8m^3 + 12m^2n + 6mn^2 + n^3$

Answer:

$8m^3 + 12m^2n + 6mn^2 + n^3$