`(20b^(3)-8b)/(4b)=`

Options

A. `5b^(2)-2b`
B. `5b^(3)-2`
C. `5b^(2)-8b`
D. `5b^(2)-2`

Answer

To simplify the expression \((20b^3 - 8b) / (4b)\), we can follow these steps:

### Step 1: Factor out the common terms in the numerator.
In the numerator \(20b^3 - 8b\), we can see that both terms have a common factor. The common factor is \(4b\).

\[ 20b^3 - 8b = 4b(5b^2 - 2) \]

### Step 2: Rewrite the expression with the factored numerator.
Now we can rewrite the original expression using the factored form of the numerator:

\[ \frac{20b^3 - 8b}{4b} = \frac{4b(5b^2 - 2)}{4b} \]

### Step 3: Cancel the common factors.
Now, we can cancel the \(4b\) in the numerator with the \(4b\) in the denominator:

\[ \frac{4b(5b^2 - 2)}{4b} = 5b^2 - 2 \]

### Step 4: Write the final simplified expression.
The simplified expression is:

\[ 5b^2 - 2 \]

### Final Answer:
Thus, the answer to the expression \((20b^3 - 8b) / (4b)\) is:

\[ 5b^2 - 2 \]

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