Question

please show me how to simplify

Answer 1

well I don't really have an equation I just need practice for an upcoming test

Answer 2

Of course! I'd be happy to help you simplify an expression. However, I'll need you to provide the specific expression or equation you'd like to simplify. Please share that, and I'll guide you through the simplification process.

Answer 3

That’s completely fine! Here are some types of expressions you might encounter, along with examples and explanations on how to simplify them.

### 1. Simplifying Algebraic Expressions

**Example:**
\[
3x + 5x
\]
**Steps:**
- Combine like terms:
\[
3x + 5x = (3 + 5)x = 8x
\]
**Simplified Expression:**
\(8x\)

### 2. Distributing (Using the Distributive Property)

**Example:**
\[
2(3x + 4)
\]
**Steps:**
- Distribute \(2\) to both terms inside the parentheses:
\[
2 \cdot 3x + 2 \cdot 4 = 6x + 8
\]
**Simplified Expression:**
\(6x + 8\)

### 3. Combining Like Terms

**Example:**
\[
4x^2 + 3x - 2x^2 + 7
\]
**Steps:**
- Combine like terms:
\[
(4x^2 - 2x^2) + 3x + 7 = 2x^2 + 3x + 7
\]
**Simplified Expression:**
\(2x^2 + 3x + 7\)

### 4. Simplifying Fractions

**Example:**
\[
\frac{6x^2}{3x}
\]
**Steps:**
- Divide coefficients and subtract exponents:
\[
\frac{6}{3} \cdot \frac{x^2}{x} = 2x
\]
**Simplified Expression:**
\(2x\)

### 5. Factoring

**Example:**
\[
x^2 - 5x + 6
\]
**Steps:**
- Factor the expression:
\[
(x - 2)(x - 3)
\]
**Simplified Expression:**
\((x - 2)(x - 3)\)

### 6. Rational Expressions

**Example:**
\[
\frac{x^2 - 1}{x + 1}
\]
**Steps:**
- Factor the numerator:
\[
\frac{(x - 1)(x + 1)}{x + 1}
\]
- Cancel the common factor:
\[
x - 1
\]
**Simplified Expression:**
\(x - 1\) (for \(x \neq -1\))

### Practice Problems
Here are some practice problems for you to try simplifying:

1. Simplify: \(5a + 3a - 2a\)
2. Simplify: \(4(2x + 3) - 5\)
3. Simplify: \(\frac{12y^3}{4y}\)
4. Factor: \(x^2 + 5x + 6\)
5. Simplify: \(\frac{2x^2 - 8}{2x}\)

Feel free to work on these and let me know if you would like me to provide solutions or explanations for any specific problem!