Which expression is equivalent to (n−4)(2n+7)

To find the expression equivalent to \((n - 4)(2n + 7)\), we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Let's expand the product:

\[
(n - 4)(2n + 7)
\]

1. **First**: Multiply the first terms of each binomial: 
\[
n \cdot 2n = 2n^2
\]

2. **Outer**: Multiply the outer terms: 
\[
n \cdot 7 = 7n
\]

3. **Inner**: Multiply the inner terms: 
\[
-4 \cdot 2n = -8n
\]

4. **Last**: Multiply the last terms: 
\[
-4 \cdot 7 = -28
\]

Now, combine these terms:

\[
2n^2 + 7n - 8n - 28 = 2n^2 - n - 28
\]

So, the expression equivalent to \((n - 4)(2n + 7)\) is:

\[
2n^2 - n - 28
\]

Would you like more details on the steps involved? 

Here are 5 questions that build on this:

1. How would you factor the expression \(2n^2 - n - 28\)?
2. What is the result if you substitute \(n = 5\) into the expanded expression?
3. How does the distributive property help in expanding binomials?
4. Can the expression \(2n^2 - n - 28\) be rewritten in vertex form?
5. What happens if one of the terms in the binomials is a fraction?

**Tip**: When expanding binomials, always make sure to combine like terms carefully to simplify the final expression.

Which expression is equivalent to (n−4)(2n+7)?

Learn how to expand and simplify the expression (n−4)(2n+7) using the distributive property, also known as the FOIL method. This step-by-step solution covers binomial expansion, algebraic simplification, and combining like terms. Suitable for students in Grades 8-10.

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