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Chapter 0: Problem 63

Find each product. $$(3 x y-1)(5 x y+2)$$

Short Answer

Expert verified
The product of the two binomials \(3xy - 1\) and \(5xy + 2\) is \(15x^2y^2 + xy - 2\).

Step by step solution

01

Multiply the First terms

The first terms in each binomial are \(3xy\) and \(5xy\). Multiplying them together gives \(15x^2y^2\).
02

Multiply the Outside terms

The outside terms in the binomials are \(3xy\) and \(2\). Multiplying these terms together gives \(6xy\).
03

Multiply the Inside terms

The inside terms are \(-1\) and \(5xy\). Multiplying these terms together gives \(-5xy\).
04

Multiply the Last terms

The last terms in the binomials are \(-1\) and \(2\). Multiplying these terms together gives \(-2\).
05

Combine the results

Add the results from Steps 1 to 4 together. The results can be added together like so: \(15x^2y^2 + 6xy - 5xy - 2\). Simplifying gives the final result: \(15x^2y^2 + xy - 2\).

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