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Chapter 5: Problem 74

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

Short Answer

Expert verified
The product of the given expression is \(x^{4} y^{4} - 10x^{2} y^{2} + 25\).

Step by step solution

01

Identify components of the binomial

In our binomial \(x^{2} y^{2}-5\), identify \(a = x^{2} y^{2}\) and \(b = 5\). These are the two components of our binomial from the given expression.
02

Apply formula

Squaring the binomial using the formula \((a - b) ^ 2 = a^2 - 2ab + b^2\), we get: \((x^{2} y^{2}-5)^{2} = (x^{2} y^{2})^2 - 2 * (x^{2} y^{2}) * 5 + 5^2\)
03

Calculate the result

Calculate the result for the previous step and finish the computation: \((x^{2} y^{2})^2 = x^{4} y^{4}\), \(2 * (x^{2} y^{2}) * 5 = 10x^{2} y^{2}\) and \(5^2 = 25\). So, the expression becomes: \(x^{4} y^{4} - 10x^{2} y^{2} + 25\)

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Most popular questions from this chapter

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I wrote a number where there is no advantage to using scientific notation instead of decimal notation.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. It is not possible to write a binomial with degree \(0 .\)

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