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Chapter 5: Problem 42

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

Short Answer

Expert verified
The product is \(6x^2 + 13xy - 5y^2\).

Step by step solution

01

Apply the 'First' rule of the FOIL method

Firstly, we multiply the first terms in each binomial. Specifically, this implies multiplying \(3 x\) and \(2 x\) which results in \(6x^2\).
02

Apply the 'Outside' and 'Inside' rules of the FOIL method

Secondly, we multiply the outer and inner terms of our binomials. The outer terms are \(3 x\) and \(5 y\) yielding a product of \(15 xy\). The inner terms are \(-y\) and \(2 x\) yielding a product of \(-2 xy\).
03

Apply the 'Last' rule of the FOIL method

Lastly, we multiply the last terms of each binomial. Specifically, \(-y\) and \(5y\) are multiplied together, giving \(-5y^2\).
04

Combine like terms

We add up all the obtained results from the previous steps which gives us \(6x^2 + 15xy -2xy -5y^2\). By combining the like terms \(15xy\) and \(-2 xy\), the final product results in \(6x^2 + 13xy - 5y^2\).

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