The expression `(3b-2)(b+5)` is euqivalent to :

Options

A. `3b^(2)-7`
B. `3b^(2)-10`
C. `3b^(2)-2b-7`
D. `3b^(2)+13b-10`

Answer

To solve the expression \((3b-2)(b+5)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Apply the Distributive Property
We start with the expression:
\[ (3b - 2)(b + 5) \]
Using the distributive property, we can expand this expression:
\[ = 3b \cdot b + 3b \cdot 5 - 2 \cdot b - 2 \cdot 5 \]

### Step 2: Multiply Each Term
Now, we will perform the multiplications:
1. \(3b \cdot b = 3b^2\)
2. \(3b \cdot 5 = 15b\)
3. \(-2 \cdot b = -2b\)
4. \(-2 \cdot 5 = -10\)

Putting these together, we have:
\[ = 3b^2 + 15b - 2b - 10 \]

### Step 3: Combine Like Terms
Next, we combine the like terms (the terms with \(b\)):
\[ = 3b^2 + (15b - 2b) - 10 \]
This simplifies to:
\[ = 3b^2 + 13b - 10 \]

### Final Result
Thus, the expression \((3b-2)(b+5)\) is equivalent to:
\[ \boxed{3b^2 + 13b - 10} \]

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