https://file.aiquickdraw.com/mathbot/file/1727326315539ogbf68b7.jpg

The equation given in your question is:

\[
5x(x + 7) - 6x(4x - 1) + 7(6x - 5)
\]

We will simplify it using the distributive law and combining like terms.

### Step 1: Apply the distributive property

- For \( 5x(x + 7) \):
  \[
  5x(x + 7) = 5x^2 + 35x
  \]

- For \( -6x(4x - 1) \):
  \[
  -6x(4x - 1) = -24x^2 + 6x
  \]

- For \( 7(6x - 5) \):
  \[
  7(6x - 5) = 42x - 35
  \]

### Step 2: Combine like terms

Now, we add all the terms together:
\[
(5x^2 + 35x) + (-24x^2 + 6x) + (42x - 35)
\]

Group the terms:
\[
(5x^2 - 24x^2) + (35x + 6x + 42x) - 35
\]

Simplify:
\[
-19x^2 + 83x - 35
\]

Thus, the simplified expression is:
\[
-19x^2 + 83x - 35
\]

Let me know if you have any questions or would like further clarification!

### Relative Questions:
1. How does the distributive property work in this example?
2. What happens when you combine terms with the same degree of \(x\)?
3. How can you simplify expressions with multiple variables?
4. What are the key steps in applying the distributive property in algebraic expressions?
5. How can understanding like terms help in solving complex algebraic equations?

**Tip:** Always check for common factors after simplification to see if further factorization is possible.

Simplify by using the distributive law and combining like terms: 5x(x + 7) - 6x(4x - 1) + 7(6x - 5)

Learn how to simplify the expression 5x(x + 7) - 6x(4x - 1) + 7(6x - 5) using the distributive property and combining like terms. Follow a step-by-step breakdown and key algebraic concepts suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation