Problem 82 - College Algebra

Question

Find each product. $$\left(7 x y^{2}-10 y\right)\left(7 x y^{2}+10 y\right)$$

Step-by-Step Solution

Answer

The product of \((7xy^{2} - 10y)\) and \((7xy^{2} + 10y)\) is \(49x^{2}y^{4} - 100y^{2}\)

Step 1: Identify the formula pattern

The given problem can be seen as the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = 7xy^{2}\) and \(b = 10y\).

Step 2: Apply the formula

Using the formula, we simply square the first term and subtract the square of the second term: \(a^2 - b^2 = (7xy^{2})^2 - (10y)^2\).

Step 3: Simplify the result

Square each term: \(49x^{2}y^{4} - 100y^{2}\).