Answer:

To find the product of the given expressions raised to the power of 3, we use the binomial expansion formula. The formula for expanding (a + b)³ is:

(a + b)³ = a³ + 3a²b + 3ab² + b³

1. (a - 5)³:

Using the formula, we have:

(a - 5)³ = a³ - 3a²(5) + 3a(5)² - 5³

Simplifying, we get:

a³ - 15a² + 75a - 125

2. (x + 7)³:

Using the formula, we have:

(x + 7)³ = x³ + 3x²(7) + 3x(7)² + 7³

Simplifying, we get:

x³ + 21x² + 147x + 343

3. (m - 2p)³:

Using the formula, we have:

(m - 2p)³ = m³ - 3m²(2p) + 3m(2p)² - (2p)³

Simplifying, we get:

m³ - 6m²p + 12mp² - 8p³

4. (k + 4p)³:

Using the formula, we have:

(k + 4p)³ = k³ + 3k²(4p) + 3k(4p)² + (4p)³

Simplifying, we get:

k³ + 12k²p + 48kp² + 64p³

5. (3n + 2p)³:

Using the formula, we have:

(3n + 2p)³ = (3n)³ + 3(3n)²(2p) + 3(3n)(2p)² + (2p)³

Simplifying, we get:

27n³ + 54n²p + 36np² + 8p³