Question

Which expression is equivalent to
–
7(2d+1)+4(
–
8d+3)?

Answer 1

To simplify the expression \(-7(2d + 1) + 4(-8d + 3)\), we can start by distributing the constants outside the parentheses.

1. Distribute \(-7\) in the first term:
\[
-7(2d + 1) = -7 \cdot 2d - 7 \cdot 1 = -14d - 7
\]

2. Distribute \(4\) in the second term:
\[
4(-8d + 3) = 4 \cdot -8d + 4 \cdot 3 = -32d + 12
\]

Now, we combine these results:
\[
-14d - 7 - 32d + 12
\]

Next, combine like terms:
- Combine the \(d\) terms:
\[
-14d - 32d = -46d
\]

- Combine the constant terms:
\[
-7 + 12 = 5
\]

Putting it all together, we have:
\[
-46d + 5
\]

Thus, the expression equivalent to \(-7(2d + 1) + 4(-8d + 3)\) is:
\[
\boxed{-46d + 5}
\]