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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 the problem

We need to square the provided expression \((x^{2} y^{2} - 5)\). When squaring a binomial expression of the form \((a - b)\) the square is equal to \(a^{2} - 2ab + b^{2}\). So, identify \(a = x^{2} y^{2}\) and \(b = 5\).
02

- Apply the formula

Substitute the values of \(a\) and \(b\) into the formula \(a^{2} - 2ab + b^{2}\). This yields \((x^{2} y^{2})^{2} - 2(x^{2} y^{2})(5) + (5)^2\).
03

- Simplify the expression

Simplify the expression to obtain \(x^{4} y^{4} - 10x^{2} y^{2} + 25\).

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Most popular questions from this chapter

Find the missing coefficients and exponents designated by question marks. $$\frac{3 x^{14}-6 x^{12}-7 x^{7}}{2 x^{7}}=-x^{7}+2 x^{5}+3$$

Subtract \(-3 x^{3}-7 x+5\) from the sum of \(2 x^{2}+4 x-7\) and \(-5 x^{3}-2 x-3\)

What is a polynomial?

The mad Dr. Frankenstein has gathered enough bits and pieces (so to speak) for \(2^{-1}+2^{-2}\) of his creature-to-be. Write a fraction that represents the amount of his creature that must still be obtained.

Exercises \(172-174\) will help you prepare for the material covered in the first section of the next chapter. In each exercise, find the product. $$(x+3)\left(x^{2}+5\right)$$
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