Mathematical Reasoning
Solve a math question
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Prompt Freeform
Prompt imageAnswer 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