Multiply. $(2 x-y)(3 x+y)$
Answer (2)
To multiply the binomials ( 2 x − y ) ( 3 x + y ) , we use the FOIL method to get 6 x 2 − x y − y 2 . First, we multiply the terms in pairs, then combine like terms to simplify. The final result is (\boxed{6x^2 - xy - y^2}}.
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6 x 2 − x y − y 2
Examples
Understanding how to multiply binomials is essential in various fields, such as physics and engineering, where you might need to calculate areas or volumes. For example, if you're designing a rectangular garden where the length is ( 3 x + y ) meters and the width is ( 2 x − y ) meters, multiplying these binomials gives you the area of the garden: 6 x 2 − x y − y 2 square meters. This algebraic skill helps in optimizing designs and resource allocation.
