Mathematical Reasoning

Solve a math question

You can query a model directly and test the results returned when using different parameter values with the Cloud console, or by calling the Vertex AI API directly. For an example of using the Vertex AI API, see Quickstart using the Vertex AI API. To view this sample in the Cloud console: Go to Google Cloud console

Prompt Freeform Answer the question in the image with step by step solution. Response Here is the step-by-step solution for multiplying and simplifying the given expressions. Problem 1: Multiply and simplify: (√x + 2√3)² Solution: We can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this expression, a = √x and b = 2√3. Square the first term (a²): (√x)² = x Find twice the product of the two terms (2ab): 2 * (√x) * (2√3) = 4 * √(x * 3) = 4√(3x) Square the second term (b²): (2√3)² = 2² * (√3)² = 4 * 3 = 12 Combine the terms: x + 4√(3x) + 12 The simplified expression is x + 12 + 4√(3x). Problem 2: Multiply and simplify: (√x + √3)(√x - √3) Solution: We can use the formula for the difference of squares: (a + b)(a - b) = a² - b². In this expression, a = √x and b = √3. Square the first term (a²): (√x)² = x Square the second term (b²): (√3)² = 3 Subtract the second result from the first (a² - b²): x - 3 The simplified expression is x - 3. Final Answers: (√x + 2√3)² = x + 12 + 4√(3x) (√x + √3)(√x - √3) = x - 3

Model: gemini-2.5-pro Temperature: 0.2 Max output tokens: 8192 TopK: 40.0 TopP: 0.95