https://file.aiquickdraw.com/mathbot/file/1725906209454j9sb5i75.jpg

Let's solve the given problem step by step.

We are asked to expand and simplify the expression:

\[
x(5x + 1) - (3x - 1)
\]

### Step 1: Expand each term.
First, distribute the \( x \) to the terms inside the parentheses:

\[
x(5x + 1) = 5x^2 + x
\]

Now, distribute the negative sign through the second parentheses:

\[
-(3x - 1) = -3x + 1
\]

### Step 2: Combine like terms.
Now we combine all the terms together:

\[
5x^2 + x - 3x + 1
\]

Simplify the linear terms (\(x\)):

\[
5x^2 + (x - 3x) + 1 = 5x^2 - 2x + 1
\]

### Final Answer:
The simplified expression is:

\[
\boxed{5x^2 - 2x + 1}
\]

Would you like a more detailed breakdown, or do you have any specific questions?

Here are some related questions you might consider:
1. How do you expand expressions with multiple parentheses?
2. What happens when you have negative terms inside parentheses?
3. How would you solve this if it were an equation instead of an expression?
4. Can this quadratic expression be factored further?
5. How do you combine like terms systematically?

**Tip**: When expanding, always distribute carefully and watch for negative signs, as they can change the entire expression.

Learn how to expand and simplify the expression x(5x + 1) - (3x - 1) in algebra. This problem focuses on using the distributive property and combining like terms to reach the simplified form. Suitable for students in 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