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The expression provided is:

\[
(6u^2 - 4u + 5)(7u - 1)
\]

We need to multiply the two binomials and then simplify the result. Let's go through it step by step using the distributive property (also known as FOIL in the case of binomials).

### Step-by-step expansion:

1. Multiply \( 6u^2 \) by both terms of \( (7u - 1) \):
   \[
   6u^2 \cdot 7u = 42u^3
   \]
   \[
   6u^2 \cdot (-1) = -6u^2
   \]

2. Multiply \( -4u \) by both terms of \( (7u - 1) \):
   \[
   -4u \cdot 7u = -28u^2
   \]
   \[
   -4u \cdot (-1) = 4u
   \]

3. Multiply \( 5 \) by both terms of \( (7u - 1) \):
   \[
   5 \cdot 7u = 35u
   \]
   \[
   5 \cdot (-1) = -5
   \]

### Now, combine all the terms:
\[
42u^3 - 6u^2 - 28u^2 + 4u + 35u - 5
\]

### Combine like terms:
\[
42u^3 + (-6u^2 - 28u^2) + (4u + 35u) - 5
\]
\[
42u^3 - 34u^2 + 39u - 5
\]

Thus, the simplified expression is:

\[
42u^3 - 34u^2 + 39u - 5
\]

Let me know if you need further details on any of the steps! Here are a few related questions to practice:

1. What is the product of \( (3u^2 + 2u - 1)(4u + 3) \)?
2. How would you expand \( (5x^2 - 3x + 4)(2x - 7) \)?
3. What is the simplified form of \( (2y + 3)(y^2 - 4y + 5) \)?
4. How does the distributive property help in multiplying polynomials?
5. Can you verify if \( (a + b)^2 = a^2 + 2ab + b^2 \) using FOIL?

**Tip:** When multiplying polynomials, group like terms carefully after expanding to avoid missing any terms!

Multiply (6u^2 - 4u + 5)(7u - 1). Simplify your answer.

This page shows the detailed steps to multiply the expressions (6u^2 - 4u + 5) and (7u - 1), using the distributive property. It explains how to expand, combine like terms, and simplify the final result. Suitable for students in Grades 8-10.

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