Question

Find the degree of the product $2xy\times 7x^2{y}^2$

• A. $14$
• B. $3$
• C. $6$
• D. $9$

Answer 1

The correct option is C $6$

First, we have to find product of $2xy$ and $7x^2{y}^2$.

$2xy\times 7x^2{y}^2=(2\times 7)\times (xy\times x^2{y}^2)$

$=14\times \left(x^{1+2}{y}^{1+2}\right)(\because a^m\times a^n=a^{m+n})$

$=14\times \left(x^3{y}^3\right)$
$=14x^3{y}^3$

$14x^3{y}^3$ is a monomial.
The degree of a monomial is the sum of the exponents of all of its variables.

Exponent of the variable $x=3$
Exponent of the variable $x=3$
Degree of the monomial $14x^3{y}^3=3+3$
$=6$

The degree of the product $2xy\times 7x^2{y}^2$ is $6$. Therefore, option (c.) is the correct answer.