Question

Identify the binomial out of the following:

• A. $3x{y}^2+5y–x^{2}y$
• B. $x^{2}y–5y–x^{2}y$
• C. $xy+yz+zx$
• D. $3x{y}^2+5y–x{y}^2$

Answer 1

The correct option is D

$3x{y}^2+5y–x{y}^2$

Explanation for correct option:

Option D: The expression given is $3x{y}^2+5y–x{y}^2$.

The given expression can be simplified as,

$3x{y}^2+5y–x{y}^2=3x{y}^2–x{y}^2+5y$

$\Rightarrow 3x{y}^2+5y–x{y}^2=\left(3–1\right)x{y}^2+5y$

$\Rightarrow 3x{y}^2+5y–x{y}^2=2x{y}^2+5y$

Which is a binomial.

Hence, option D is the correct option.

Explanation for incorrect options:

Option A: The expression given is $3x{y}^2+5y–x^{2}y$.

The given expression cannot be simplified further.

So, the given expression is a trinomial.

Hence, option A is incorrect.

Option B: The expression given is $x^{2}y–5y–x^{2}y$.

The given expression can be simplified as,

$x^{2}y–5y–x^{2}y=x^{2}y–x^{2}y–5y$

$\Rightarrow x^{2}y–5y–x^{2}y=–5y$

Which is a monomial.

Hence, option B is incorrect.

Option C: The expression given is $xy+yz+zx$.

The given expression cannot be simplified further.

So, the given expression is a trinomial.

Hence, option C is incorrect.