Image with math problem

Let's simplify the given expression:

$$\frac{8m + 8n}{a^2} \cdot \frac{5a^{10}}{m^2 - n^2}$$

First, we can factor out 8 from the numerator in the first fraction:

$$\frac{8(m + n)}{a^2} \cdot \frac{5a^{10}}{m^2 - n^2}$$

Next, we can factor the denominator in the second fraction using the difference of squares:

$$m^2 - n^2 = (m + n)(m - n)$$

So, the expression becomes:

$$\frac{8(m + n)}{a^2} \cdot \frac{5a^{10}}{(m + n)(m - n)}$$

Now we can cancel out the common factor $$(m + n)$$ from the numerator and denominator:

$$\frac{8}{a^2} \cdot \frac{5a^{10}}{(m - n)}$$

Now, multiply the numerators and the denominators:

$$\frac{8 \cdot 5a^{10}}{a^2(m - n)}$$

$$\frac{40a^{10}}{a^2(m - n)}$$

Finally, we can simplify the expression by dividing $$a^{10}$$ by $$a^2$$:

$$a^{10} / a^2 = a^{10-2} = a^8$$

So, the simplified expression is:

$$\frac{40a^8}{m - n}$$

Ответ: $$\frac{40a^8}{m - n}$$