Short Answer 
Louise’s response lacks the crucial term “30×3,” necessary for squaring the binomial. The correct approach involves using the distributive property or applying the perfect square trinomial formula to accurately calculate the square of a binomial.
Step 1: Identify the Error
Louise’s response contains a mistake as she does not mention the term 30×3, which is crucial to the solution. This term is essential for accurately squaring the binomial. It’s important to carefully review each element involved in the problem to ensure all necessary components are included for an accurate calculation.
Step 2: Use the Distributive Property
To properly square a binomial, write down the product of the binomial times itself. For example, if the binomial is (a + b), then you need to calculate (a + b)(a + b). Utilize the distributive property to multiply each term in the first binomial by each term in the second binomial, which gives you:
- a² + 2ab + b²
Step 3: Apply the Perfect Square Trinomial Formula
Another effective method is to use the formula for a perfect square trinomial. This formula states that (a + b)² = a² + 2ab + b². Louise could have directly applied this formula to find the result faster, ensuring that she uses the structure of binomials to arrive at the correct answer.