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Chapter 5: Problem 55

Find each product. $$(a b+1)(a b-1)$$

Short Answer

Expert verified
The product of \( (a b+1)(a b-1) \) is \( a^2 b^2 - 1 \).

Step by step solution

01

Identify the special format

The given expression \( (a b+1)(a b-1) \) is of the format \( (a+b)(a-b) \). This is a special format that can be simplified according to the formula given above, without needing the regular process of FOIL.
02

Apply the formula

Replacing \( a \) with \( a b \), and \( b \) with \( 1 \), the resulting expression according to the formula becomes: \( (a b)^2 - (1)^2 \).
03

Simplify the expression

The expression simplifies to \( a^2 b^2 - 1 \).

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Most popular questions from this chapter

Exercises \(110-112\) will help you prepare for the material covered in the next section. In each exercise, perform the long division without using a calculator, and then state the quotient and the remainder. $$2 4 \longdiv { 2 9 5 8 }$$

Use a vertical format to find each product. $$\begin{array}{r}n^{4}-n^{3}+n^{2}-n+1 \\\2 n+3 \\\\\hline\end{array}$$

How do you know if a number is written in scientific notation?

Explain how to multiply monomials. Give an example.

Simplify: \(24+8 \cdot 3+28 \div(-7)\).
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