Question

$\left(A{x}^{3}y\right)\text{and}\left(\frac{4}{3}x\right)\left(x^{2}y\right)\text{are like terms where}\text{A is the numerical factor of that term.}\text{Then, which of the following is correct ?}$

• A. $\text{A should be equal to}\frac{4}{3}$
• B. $\text{A can take any value except}\frac{4}{3}$
• C. $\text{A should be equal to}\frac{3}{4}$
• D. $\text{A can take any numerical value}$

Answer 1

The correct option is D $\text{A can take any numerical value}$

We know that like terms have the same variables and the powers of these variables are also same.
Coefficients of like terms need not be the same.

$\left(\frac{4}{3}x\right)\left(x^{2}y\right)\text{can be written as}\frac{4}{3}{x}^{3}y.$
$\text{So,}\left(A{x}^{3}y\right)\text{and}\left(\frac{4}{3}{x}^{3}y\right)\text{are like terms.}$

Therefore, A can take any numerical value.