Which of the following expressions are binomials?

$7 x + 8 x y$

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$1 + 2 x + 3 y$

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$3 x + 7 x y + y x$

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$3 x + 2 y$

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Solution

The correct options are
A
$7 x + 8 x y$

C
$3 x + 7 x y + y x$

D
$3 x + 2 y$

A binomial is an algebraic expression consisting of two unlike terms.

A ) $7 x + 8 x y$ has two unlike terms. So, it is a binomial.
B) $1 + 2 x + 3 y$ has three unlike terms. So, it is not a binomial.
C) $3 x + 7 x y + y x$ has three terms but can be simplified further as $3 x + 8 y x$ as ( $7 x y$ and $y x$ are like terms). Hence it is a binomial.
D) $3 x + 2 y$ has two unlike terms. So, it is a binomial.
Hence, options A, C, D are correct.

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