Question

Identify like terms in the following:

$-x{y}^2,-4y{x}^2,8x^2,2x{y}^2,7y,-11x^2,-100x,-11yx,20x^{2}y,-6x^2,y,2xy,3x$

Answer 1

Define like terms and identify them:

The two or more algebraic terms having the same constituent variables and the same power for each variable are said to be like terms.

The given expressions are,

$-x{y}^2,-4y{x}^2,8x^2,2x{y}^2,7y,-11x^2,-100x,-11yx,20x^{2}y,-6x^2,y,2xy,3x$

Here, the terms having only $x$, only $y$, $xy$, $x^{2}y$ or $x{y}^2$ are the like terms.

So, the like terms of the given data are,

1. $-100x,3x$
2. $7y,y$
3. $-11yx,2xy$ $\left[\because xy=yx\right]$
4. $8x^2,-11x^2,-6x^2$
5. $-4y{x}^2,20x^{2}y$ $\left[\because x^{2}y=y{x}^2\right]$
6. $-x{y}^2,2x{y}^2$

Hence, the like terms are $\left(-100x,3x\right),\left(7y,y\right),\left(-11yx,2xy\right),\left(8x^2,-11x^2,-6x^2\right),\left(-4y{x}^2,20x^{2}y\right)$ and $\left(-x{y}^2,2x{y}^2\right)$.