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Chapter 5: Problem 42

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

Short Answer

Expert verified
The product of the given binomials \((3x-y)\) and \((2x+5y)\) is \(6x^2+13xy-5y^2\).

Step by step solution

01

Identify the binomials

The binomials given in the exercise are \((3x-y)\) and \((2x+5y)\). These two will be multiplied.
02

Apply Distributive Property or FOIL method

FOIL is an acronym for First, Outer, Inner, and Last. It is a method for multiplying binomials.\[ (3x-y)(2x+5y) \]First: Multiply the first terms in each binomial: \(3x * 2x = 6x^2\).\[ 6x^2 \]Outer: Multiply the outer terms in the original expression: \(3x * 5y = 15xy\).\[ 6x^2+15xy\]Inner: Multiply the inner terms: \(-y * 2x = -2xy\).\[ 6x^2+15xy-2xy\]Last: Multiply the last terms: \(-y * 5y = -5y^2\). \[6x^2+15xy-2xy-5y^2 \]
03

Simplify the expression

Combine like terms, if any. In this case, \(15xy\) and \(-2xy\) are like terms. Combining these gives us \(13xy\). So the simplified form of the expression is:\[ 6x^2+13xy-5y^2 \]

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