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Chapter 5: Problem 56

Find each product. $$(a b+2)(a b-2)$$

Short Answer

Expert verified
The product of the binomials \(ab+2\) and \(ab-2\) is \(a^2b^2 - 4\).

Step by step solution

01

Multiply the binomials

To find the product, you multiply each term of the first binomial by each term of the second. Given (ab+2)(ab-2), specifically, it results in \(ab * ab - ab*2 + 2*ab - 2*2\).
02

Simplify the equation

The equation simplifies to \(a^2b^2 - 2ab + 2ab - 4\). The terms -2ab and +2ab cancel out.
03

Final Simplification

After cancellation of similar terms, the equation simplifies to \(a^2b^2 - 4\), which is the final product.

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