Question

Simplify the following expressions.
1. 5(3s - 2) + 12x
2. 7(3y -5) + 2 (4y + 3)

Answer 1

Let's simplify each expression step by step:

1. **Expression: \(5(3s - 2) + 12x\)**

Start by distributing the \(5\) into the parentheses:
\[
5 \times 3s - 5 \times 2 = 15s - 10
\]
Now, substitute this back into the expression:
\[
15s - 10 + 12x
\]
The simplified expression is:
\[
15s + 12x - 10
\]

2. **Expression: \(7(3y - 5) + 2(4y + 3)\)**

First, distribute the \(7\) and \(2\) into their respective parentheses:
\[
7 \times 3y - 7 \times 5 = 21y - 35
\]
\[
2 \times 4y + 2 \times 3 = 8y + 6
\]
Now, combine these two results:
\[
21y - 35 + 8y + 6
\]
Combine like terms:
\[
(21y + 8y) + (-35 + 6) = 29y - 29
\]
The simplified expression is:
\[
29y - 29
\]

In summary:

1. \(15s + 12x - 10\)
2. \(29y - 29\)