To simplify the expression $3(4x - y + 7)$, we need to distribute the 3 across each term inside the parentheses:

$3(4x - y + 7) = 3 \times 4x - 3 \times y + 3 \times 7$

Now, perform the multiplication:

$= 12x - 3y + 21$

So, the simplified expression is:

$12x - 3y + 21$

Would you like further details on the distribution process or have any other questions?

Here are 5 related questions to practice:

1. Simplify $2(5a + 3b - 4)$.
2. Expand $6(3x - 2y + 1)$.
3. Factor out the greatest common factor in $15x - 9y + 6$.
4. Simplify $4(2x + y - 3) + 5x$.
5. Solve for $x$ in the equation $3(2x - 1) = 9$.

Tip: When distributing, make sure to multiply each term inside the parentheses by the factor outside.