Question

Find the product: -mnp(3m - 5n + 7p) = _____.

Option 1: -3m²np + 5mn²p - 7mnp²
Option 2: -3m²np - 5mn²p + 7mnp²
Option 3: -3m²np + 5mn²p + 7mnp²
Option 4: -3m²np - 5mn²p - 7mnp²

Answer 1

After distributing the term -mnp across each term within the parentheses, the result is -3m²np - 5mn²p + 7mnp². Therefore, the correct option is Option 2.

Step-by-step explanation:

To find the product of -mnp and (3m - 5n + 7p), we need to distribute -mnp across each term in the parentheses. The operation we perform is essentially multiplying -mnp by each term within the parentheses, one at a time:

• -mnp × 3m = -3m²np
• -mnp × -5n = 5mn²p
• -mnp × 7p = -7mnp²

Now, combining all these results, we have the equation:

-mnp(3m - 5n + 7p) = -3m²np + 5mn²p - 7mnp²

Hence, the correct option is:

Option 2: -3m²np - 5mn²p + 7mnp²