Problem 40 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The product is: \(4 - y^{10}\).

Step 1: Recognize the pattern

Recognize that the given expression fits the pattern of a difference of squares, \(a^2 - b^2\), which can be factored as \((a - b)(a + b)\). In this case, \(a = 2\) and \(b = y^{5}\).

Step 2: Apply the formula

Apply the formula of difference of squares to the given expression. This results in the following: \((2 - y^{5})(2 + y^{5}) = a^2 - b^2 = 2^2 - (y^{5})^2\).

Step 3: Simplify the equation

Simplify the equation by performing the relevant mathematical operations which results in the following: \(4 - y^{10}\).