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Chapter 5: Problem 43

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

Short Answer

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

Step by step solution

01

Distribute the first term of the first polynomial to the second polynomial

To begin with, multiply the first term of the first polynomial \(3xy\) by each term in the second polynomial. That is, \(3xy*5xy\) and \(3xy*2\). This gives \(15x^2y^2\) and \(6xy\).
02

Distribute the second term of the first polynomial to the second polynomial

Next, multiply the second term of the first polynomial \(-1\) by each term in the second polynomial. That is, \(-1*5xy\) and \(-1*2\). This gives \(-5xy\) and \(-2\).
03

Combine the products

Now, combine the products obtained from the two steps above. \(15x^2y^2 + 6xy - 5xy - 2\). Collect like terms \(6xy - 5xy\) that simplifies to \(xy\). Hence, the final result is \(15x^2y^2 + xy - 2\).

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