Expand and fully simplify $$ x(4 x-2)+x(3 x+7) $$

Question

UpStudy AI · Accepted Answer

To expand and fully simplify the expression $$ x(4x - 2) + x(3x + 7) $$, follow these steps:

### Step 1: Distribute $$ x $$ to Each Term Inside the Parentheses

Apply the distributive property, which states that $$ a(b + c) = ab + ac $$.

$$
x(4x - 2) + x(3x + 7) = x \cdot 4x + x \cdot (-2) + x \cdot 3x + x \cdot 7
$$

### Step 2: Perform the Multiplications

$$
= 4x^2 - 2x + 3x^2 + 7x
$$

### Step 3: Combine Like Terms

Identify and combine the terms that have the same power of $$ x $$:

- **Quadratic Terms ($$ x^2 $$)**:
  $$
  4x^2 + 3x^2 = 7x^2
  $$

- **Linear Terms ($$ x $$)**:
  $$
  -2x + 7x = 5x
  $$

### Step 4: Write the Simplified Expression

$$
7x^2 + 5x
$$

**Final Answer:**  
$$\boxed{7x^2 + 5x}$$
$$7x^2 + 5x$$

Expand and fully simplify \( x(4 x-2)+x(3 x+7) \)