Problem 101 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The square of the binomial difference \(3x - 2y\) is \(9x^2 - 12xy + 4y^2\).

Step 1: Identify a Binomial Difference

A binomial difference is an algebraic expression containing two terms which are subtracted. It takes the form: \(a-b\). We will use \(3x - 2y\) as our example for this exercise.

Step 2: Apply the Square Formula

The square of a binomial difference can be found using the formula: \((a - b)^2= a^2 - 2ab + b^2 \). Apply this formula to the chosen binomial difference. Replace \(a\) with \(3x\) and \(b\) with \(2y\) in the formula.

Step 3: Calculate the Square

Squaring each term and applying the formula gives: \((3x - 2y)^2 = (3x)^2 - 2(3x)(2y) + (2y)^2 = 9x^2 - 12xy + 4y^2\).