Homework

Answer the question in the image with step by step solution.

Here is the step-by-step solution to multiply and simplify the given expressions.

Problem 1: (√x + 2√3)²

Step 1: Use the formula for squaring a binomial. The expression is in the form (a + b)², where a = √x and b = 2√3. The formula for squaring a binomial is: (a + b)² = a² + 2ab + b²

Step 2: Substitute 'a' and 'b' into the formula. (√x + 2√3)² = (√x)² + 2(√x)(2√3) + (2√3)²

Step 3: Simplify each term. * (√x)² = x * 2(√x)(2√3) = 4√(x * 3) = 4√(3x) * (2√3)² = 2² * (√3)² = 4 * 3 = 12

Step 4: Combine the simplified terms. x + 4√(3x) + 12

Final Answer: (√x + 2√3)² = x + 4√(3x) + 12

Problem 2: (√x + √3)(√x - √3)

Step 1: Use the difference of squares formula. The expression is in the form (a + b)(a - b), where a = √x and b = √3. The formula for the difference of squares is: (a + b)(a - b) = a² - b²

Step 2: Substitute 'a' and 'b' into the formula. (√x + √3)(√x - √3) = (√x)² - (√3)²

Step 3: Simplify each term. * (√x)² = x * (√3)² = 3

Step 4: Combine the simplified terms. x - 3

Final Answer: (√x + √3)(√x - √3) = x - 3