Raghav had ₹ `(6x^(3) + 2x^(2) + 3x)` and he bought `(4x^(2) + 3)` shirts. The price of each shirt is ₹ (x + 5). How much money is left with Raghav?

Options

A. `₹ (2x^(3) - 18x^(2) -15)`
B. `₹ (4x^(2) + 2x +3)`
C. `₹( x^(3)-3x)`
D. `₹( 2x^(3) + 2x^(2) -15)`

Answer

To find out how much money is left with Raghav after buying the shirts, we will follow these steps:

### Step 1: Determine the total amount Raghav had initially.
Raghav had ₹ (6x³ + 2x² + 3x).

### Step 2: Calculate the total cost of the shirts.
Raghav bought (4x² + 3) shirts, and the price of each shirt is (x + 5) rupees.

To find the total cost of the shirts, we multiply the number of shirts by the price of each shirt:
\[ \text{Total Cost} = \text{Number of Shirts} \times \text{Price per Shirt} \]
\[ \text{Total Cost} = (4x² + 3)(x + 5) \]

### Step 3: Expand the expression for the total cost.
Using the distributive property (also known as the FOIL method for binomials):
\[ (4x² + 3)(x + 5) = 4x² \cdot x + 4x² \cdot 5 + 3 \cdot x + 3 \cdot 5 \]
\[ = 4x³ + 20x² + 3x + 15 \]

### Step 4: Subtract the total cost from the initial amount.
Now, we will subtract the total cost from the initial amount Raghav had:
\[ \text{Money Left} = \text{Initial Amount} - \text{Total Cost} \]
\[ \text{Money Left} = (6x³ + 2x² + 3x) - (4x³ + 20x² + 3x + 15) \]

### Step 5: Simplify the expression.
Now we will combine like terms:
\[ \text{Money Left} = (6x³ - 4x³) + (2x² - 20x²) + (3x - 3x) - 15 \]
\[ = 2x³ - 18x² - 15 \]

### Final Answer:
Thus, the amount of money left with Raghav is:
\[ \text{Money Left} = 2x³ - 18x² - 15 \]

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