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Chapter 5: Problem 73

Find each product. $$\left(x^{2} y^{2}-3\right)^{2}$$

Short Answer

Expert verified
The product of \((x^{2}y^{2}-3)^{2}\) results in \(x^{4}y^{4} -6x^{2}y^{2} +9\).

Step by step solution

01

Identify terms

Identify the factors of the binomial - in this instance, the first factor, \(a\), is \(x^2y^2\) and the second factor, \(b\), is 3.
02

Apply the formula

The expression \((x^{2}y^{2}-3)^{2}\) can be rewritten as \((a-b)^{2}\) where \(a=x^{2}y^{2}\) and \(b=3\). So now, plug these into the formula for the binomial square which is \(a^2 - 2ab + b^2\). This will become: \((x^{2}y^{2})^{2} - 2(x^{2}y^{2})(3) +(3)^{2}\).
03

Simplify

Simplify this expression. The first term is \(x^{4}y^{4}\), the second term is \(-6x^{2}y^{2}\), and the third term is \(9\). Hence the solution is: \(x^{4}y^{4} -6x^{2}y^{2} +9\)

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