minus, 7, left parenthesis, 5, s, minus, t, right parenthesis, plus, 5, t, minus, 7, left parenthesis, 3, t, minus, 4, s, right parenthesis−7(5s−t)+5t−7(3t−4s)

Let's simplify the expression step by step.

The given expression is:
\[
-7(5s - t) + 5t - 7(3t - 4s)
\]

### Step 1: Distribute \(-7\) in both parentheses.

1. Distribute \(-7\) to \((5s - t)\):
   \[
   -7(5s - t) = -35s + 7t
   \]

2. Distribute \(-7\) to \((3t - 4s)\):
   \[
   -7(3t - 4s) = -21t + 28s
   \]

Now the expression becomes:
\[
-35s + 7t + 5t - 21t + 28s
\]

### Step 2: Combine like terms.

1. Combine terms with \(s\): \(-35s + 28s = -7s\)
2. Combine terms with \(t\): \(7t + 5t - 21t = -9t\)

### Final Simplified Expression:
\[
-7s - 9t
\]

Would you like any further details or have any questions?

Here are 5 related questions to expand on the topic:
1. How do you simplify expressions with multiple variables?
2. What are like terms, and why is it important to combine them?
3. How can distributing negative values affect the final expression?
4. What steps should be followed to simplify a complex algebraic expression?
5. How can we verify if the simplification of an expression is correct?

**Tip:** Always keep track of your signs (positive/negative) when distributing and combining terms to avoid mistakes.

minus, 7, left parenthesis, 5, s, minus, t, right parenthesis, plus, 5, t, minus, 7, left parenthesis, 3, t, minus, 4, s, right parenthesis

Learn how to simplify the expression -7(5s - t) + 5t - 7(3t - 4s) with a step-by-step solution. This problem uses algebraic concepts such as the distributive property and combining like terms, ideal for students in Grades 7-9.

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