a. How are these two equations related? b. Explain the relationship between the polynomial identities 𝑥2 − 1 = (𝑥 + 1)(𝑥 − 1) and
Based on the work in this lesson, students can convert differences of squares into products (and vice versa) using
𝑥2 − 𝑎2 = (𝑥 − 𝑎)(𝑥 +𝑎).
If 𝑥, 𝑎, and 𝑛 are integers with (𝑥 − 𝑎) ≠ ±1 and 𝑛 > 1, then numbers of the form 𝑥𝑛 − 𝑎𝑛 are not prime because
𝑥n − 𝑎n = (𝑥 − 𝑎)(𝑥n-1 + 𝑎𝑥n-2 + 𝑎2𝑥n-3 + ⋯ + 𝑎n-2𝑥 + 𝑎n-1).
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.