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Chapter 5: Problem 52

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

Short Answer

Expert verified
The product we are looking for is \(x^4 - 2x^2y^2 + y^4\)

Step by step solution

01

Applying the square of a binomial formula

The first step involves applying the square of a binomial formula. This becomes \((x^2-y^2)^2 = (x^2)^2 - 2*(x^2)*(y^2) + (y^2)^2).
02

Calculating the squares

Next, calculate the square of each term inside the parentheses. This results in \(x^4 - 2x^2y^2 + y^4\).

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Most popular questions from this chapter

Perform the indicated operations. $$(y+6)^{2}-(y-2)^{2}$$

Perform the indicated computations. Express answers in scientific notation. $$\left(2 \times 10^{2}\right)\left(2.6 \times 10^{-3}\right) \div\left(4 \times 10^{3}\right)$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)^{2}\) b. \((x+5)^{2}\)

Explain the difference between \((-7)^{0}\) and \(-7^{0}\).

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