Problem 40 - College Algebra

Question

Find each product. $$\left(2-y^{5}\right)\left(2+y^{5}\right)$$

Step-by-Step Solution

Answer

The solution to the given problem is \(4 - y^{10}\).

Step 1: Identifying the Formula

To simplify the given expression, one may recognize a pattern within the binomial terms that resembles a certain algebraic formula pattern: \[a^2 - b^2\], which can simplify to \((a+b)(a-b)\). Compare this with the given exercise where \(a\) is \(2\) and \(b\) is \(y^5\).

Step 2: Applying the Formula

Apply the known formula \((a+b)(a-b) = a^2 - b^2\), replace \(a\) with \(2\) and \(b\) with \(y^5\).

Step 3: Final Calculation

By calculation \(a^2 - b^2\) gives \((2)^2 - (y^5)^2 = 4 - y^{10}\).