(2x + 3)(3x - 1) = ?

Options

A. `(6x^(2) + 8x - 3)`
B. `(6x^(2) + 7x - 3)`
C. `(6x^(2) - 7x - 3`
D. `(6x^(2) - 7x + 3)`

Answer

To solve the expression \((2x + 3)(3x - 1)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step breakdown:

### Step 1: Distribute \(2x\) to both terms in the second bracket
We start by multiplying \(2x\) with each term in the second bracket \((3x - 1)\):
\[ 2x \cdot 3x + 2x \cdot (-1) \]
This gives us:
\[ 6x^2 - 2x \]

### Step 2: Distribute \(3\) to both terms in the second bracket
Next, we multiply \(3\) with each term in the second bracket \((3x - 1)\):
\[ 3 \cdot 3x + 3 \cdot (-1) \]
This gives us:
\[ 9x - 3 \]

### Step 3: Combine all the terms
Now, we combine all the terms we have obtained from the previous steps:
\[ 6x^2 - 2x + 9x - 3 \]

### Step 4: Combine like terms
We combine the like terms \(-2x\) and \(9x\):
\[ 6x^2 + (9x - 2x) - 3 = 6x^2 + 7x - 3 \]

### Final Answer
Thus, the final result of \((2x + 3)(3x - 1)\) is:
\[ \boxed{6x^2 + 7x - 3} \]

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