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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 \((x^{2} y^{2}-3)^{2}\) is \(x^4y^4 - 6x^2y^2 + 9\)

Step by step solution

01

Identify the Binomial

Firstly, identify the binomial (a - b) which will be squared. Here, it is \((x^{2} y^{2} - 3)\).
02

Apply Square of Binomial Formula

Next, apply the square of binomial formula, which says \((a - b)^2 = a^2 - 2ab + b^2\). Here, 'a' is \(x^{2} y^{2}\) and 'b' is 3.
03

Substitute and Calculate

After substitution, we have \((x^2y^2)^2 - 2*(x^2y^2)*3 + 3^2\). This simplifies to \(x^4y^4 - 6x^2y^2 + 9\).

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Most popular questions from this chapter

Use a vertical format to find each product. $$\begin{array}{r}7 x^{3}-5 x^{2}+6 x \\\3 x^{2}-4 x \\\\\hline\end{array}$$

Explain how to divide a polynomial that is not a monomial by a monomial. Give an example.

Use a vertical format to find each product. $$\begin{array}{r} 9 y^{3}-7 y^{2}+5 y \\ 3 y^{2}+5 y \\ \hline \end{array}$$

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