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To simplify the given expression \( 14b(a + c) - 7(a + c) \), follow these steps:

1. **Factor out the common term \((a + c)\):**
   \[
   14b(a + c) - 7(a + c) = (a + c)(14b - 7)
   \]

2. **Simplify the expression inside the parentheses:**
   \[
   14b - 7 = 7(2b - 1)
   \]

3. **Substitute this back into the factored expression:**
   \[
   (a + c)(14b - 7) = (a + c)(7(2b - 1))
   \]

4. **Distribute the 7:**
   \[
   (a + c)(7(2b - 1)) = 7(a + c)(2b - 1)
   \]

Thus, the simplified form of the expression is:
\[
7(a + c)(2b - 1)
\]

Would you like further details or have any questions about the steps taken?

Here are some related questions for further practice:

1. Simplify \( 5x(3y + 4) - 2(3y + 4) \).
2. Factor the expression \( 6m(n + p) - 3(n + p) \).
3. Expand and simplify \( (x + 3)(2x - 5) \).
4. Simplify \( 8k(2l - 3) - 4(2l - 3) \).
5. Factor \( 9p(q + r) - 3(q + r) \).

**Tip:** When simplifying expressions, always look for common factors that can be factored out to make the process easier.

Simplify the expression 14b(a + c) - 7(a + c).

Learn how to simplify the algebraic expression 14b(a + c) - 7(a + c) by factoring out common terms and applying the distributive property. This step-by-step guide covers key algebra concepts for students in Grades 8-10.

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