Question

Identify like terms in the following:

$10pq,7p,8q,-p^2{q}^2,-7qp,-100q,-23,12q^2{p}^2,-5p^2,41,2405p,78qp,13p^{2}q,q{p}^2,701p^2$

Answer 1

Define like terms and identify them:

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

The given expressions are,

$10pq,7p,8q,-p^2{q}^2,-7qp,-100q,-23,12q^2{p}^2,-5p^2,41,2405p,78qp,13p^{2}q,q{p}^2,701p^2$

Here, the terms having no variables, only $p$, only $q$, $pq$, $p^2$, $p^{2}q$ or $p^2{q}^2$ are the like terms.

So, the like terms of the given data are,

1. $-23,41$
2. $7p,2405p$
3. $8q,-100q$
4. $10pq,-7qp,78qp$ $\left[\because pq=qp\right]$
5. $-5p^2,701p^2$
6. $13p^{2}q,q{p}^2$ $\left[\because p^{2}q=q{p}^2\right]$
7. $-p^2{q}^2,12q^2{p}^2$ $\left[\because p^2{q}^2=q^2{p}^2\right]$

Hence, the like terms are $\left(-23,41\right),\left(7p,2405p\right),\left(8q,-100q\right),\left(10pq,-7qp,78qp\right),\left(-5p^2,701p^2\right),\left(13p^{2}q,q{p}^2\right)$ and $\left(-p^2{q}^2,12q^2{p}^2\right)$.