Question

(m+2n)^3= Пожалуйста

Answer 1

Ответ:

Пошаговое объяснение:

(m+2n)³= m³+9m²n+27mn²+27n³

Answer 2

To expand the expression $(m + 2n)^3$, we'll use the binomial theorem. The binomial theorem states that for any real numbers $a$ and $b$ and a positive integer $n$, the following formula holds:

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

where $\binom{n}{k}$ represents the binomial coefficient, which is given by $\frac{n!}{k!(n-k)!}$.

In our case, $a = m$ and $b = 2n$, and $n = 3$, so the expression becomes:

$(m + 2n)^3 = \sum_{k=0}^{3} \binom{3}{k} m^{3-k} (2n)^k$

Let's calculate each term:

1. $k = 0$: $\binom{3}{0} m^{3-0} (2n)^0 = 1 \cdot m^3 \cdot 1 = m^3$

2. $k = 1$: $\binom{3}{1} m^{3-1} (2n)^1 = 3 \cdot m^2 \cdot 2n = 6mn$

3. $k = 2$: $\binom{3}{2} m^{3-2} (2n)^2 = 3 \cdot m \cdot 4n^2 = 12n^2m$

4. $k = 3$: $\binom{3}{3} m^{3-3} (2n)^3 = 1 \cdot 1 \cdot 8n^3 = 8n^3$

Now, we add up all these terms:

$(m + 2n)^3 = m^3 + 6mn + 12n^2m + 8n^3$

And that's the expanded form of $(m + 2n)^3$.