Question

Find the like terms from the given terms and add them:
$4xyz,2x^2{y}^2,3x^2{y}^2,4x^2,9x^2{y}^2,18x^2,6xyz,10x^2,7xyz$

• A. (1) 11xyz
  (2) $12x^2{y}^2$
  (3) $32x^2$
• B. (1) 17xyz
  (2) $14x^2{y}^2$
  (3) $32x^2$
• C. (1) -17xyz
  (2) $14x^2{y}^2$
  (3) $28x^2$
• D. none

Answer 1

The correct option is B (1) 17xyz

(2) $14x^2{y}^2$
(3) $32x^2$
We know that like terms are terms whose variables (and their exponents such as the $2$ in $x^2$) are the same.

In the given terms $4xyz,2x^2{y}^2,3x^2{y}^2,4x^2,9x^2{y}^2,18x^2,6xyz,10x^2,7xyz$, the like terms are as follows:

(i) $4xyz,6xyz,7xyz$

(ii) $2x^2{y}^2,3x^2{y}^2,9x^2{y}^2$

(iii) $4x^2,18x^2,10x^2$

Now, adding the like terms, we get:

(i) $4xyz+6xyz+7xyz=17xyz$

(ii) $2x^2{y}^2+3x^2{y}^2+9x^2{y}^2=14x^2{y}^2$

(iii) $4x^2+18x^2+10x^2=32x^2$

Hence, after adding the like terms we get $17xyz,14x^2{y}^2,32x^2$.