Problem 77 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of \((x^{2} y^{2}-5)^{2}\) is \(x^{4}y^{4}-10x^{2}y^{2}+25\)

Step 1: Identify the values of a and b

In the binomial \((x^{2} y^{2}-5)^{2}\), capture the values of a and b. Here, \(a = x^{2} y^{2}\) and \(b = 5\).

Step 2: Apply the formula for the square of a binomial

Use the formula \((a - b)^2 = a^2 - 2ab + b^2\). Replace \(a\) with \(x^{2} y^{2}\) and \(b\) with 5.

Step 3: Insert values into the formula

The equation now reads \((x^{2}y^{2})^{2}-2*(x^{2}y^{2})*5+5^{2}\).

Step 4: Simplification

After simplifying, we have \(x^{4}y^{4}-10x^{2}y^{2}+25\)