Problem 95 - College Algebra

Question

Explain how to square a binomial difference. Give an example with your explanation.

Step-by-Step Solution

Answer

To square a binomial difference such as \((x - 3)^2\), apply the square of binomial formula to get \(x^2 - 2 * x * 3 + 9\), which simplifies to \(x^2 - 6x + 9\).

Step 1: Identify the Binomial Difference

First, it is necessary to identify the binomial difference that you need to square. For example, consider the binomial difference \((x-3)\), where \(x\) and \(3\) are your \(a\) and \(b\) variables respectively.

Step 2: Apply the Square of Binomial Formula

After identifying the binomial difference, the next step is to apply the square of binomial formula. Using the values from our example, we would have to perform the following operations: Square \(a\), then subtract \(2 * a * b\), and finally add the square of \(b\). It would look like this: \((x - 3)^2 = x^2 - 2 * x * 3 + 3^2 \).

Step 3: Simplify the Equation

After applying the formula, the final step in squaring a binomial difference is to simplify the equation. Using our example, the simplified form would be \(x^2 - 6x + 9 \). This is the squared form of the given binomial difference \((x - 3)^2 \).