Round #648

Simplify the expression 3x squared times 4x cubed.

To simplify the expression \(3x^2 \times 4x^3\), you can follow these steps: 1. Multiply the coefficients (the numbers in front of the variables): \(3 \times 4 = 12\). 2. Add the exponents of the variable \(x\) since they are being multiplied: \(x^2 \times x^3 = x^{2+3} = x^5\). So, the simplified expression is: \[12x^5\]

To simplify the expression \(3x^2 \times 4x^3\), we need to follow these steps: 1. Multiply the coefficients (the numerical parts). 2. Add the exponents of the variable \(x\) since they are being multiplied. Let's implement this in C# using basic arithmetic operations and string manipulation to handle the expression. ```csharp using System; class ExpressionSimplifier { public static string SimplifyExpression(string expression) { // Split the expression into coefficient and variable parts var parts = expression.Split('x'); int coefficient = int.Parse(parts[0]); int exponent = 0; // Check if there is an exponent in the variable part if (parts[1].Contains('^')) { exponent = int.Parse(parts[1].Split('^')[1]); } else { exponent = 1; } // Multiply the coefficient by 4 coefficient *= 4; // Add the exponents (2 + 3) exponent += 2 + 3; // Return the simplified expression as a string return $"{coefficient}x^{exponent}"; } } class Program { static void Main() { string expression = "3x^2 * 4x^3"; string simplifiedExpression = ExpressionSimplifier.SimplifyExpression(expression); Console.WriteLine(simplifiedExpression); // Output: 12x^5 } } ``` ### Explanation: 1. **Splitting the Expression**: The expression is split into two parts using the `Split('x')` method, which separates the coefficient and the variable part. 2. **Parsing Coefficient**: The coefficient part is parsed from a string to an integer. 3. **Handling Exponents**: - If the exponent is explicitly given (e.g., \(x^3\)), it is parsed from the string. - If no exponent is given (e.g., \(x\)), it defaults to 1. 4. **Multiplying Coefficients**: The coefficient is multiplied by 4 as per the expression. 5. **Adding Exponents**: The exponents of both parts are added together. 6. **Returning the Result**: The simplified expression is constructed and returned in the form \( \text{coefficient}x^{\text{exponent}} \). This implementation handles the basic arithmetic and string manipulation required to simplify the given expression.