Chapter 4.1, Problem 6OE

To determine

The similar monomials among these monomials $u{v}^2,-3u^{2}v,-u^3,\frac{3}{2}u{v}^2,uv,4,2vu,v^3,u^{2}v,-7$ .

Answer to Problem 6OE

  $\left(u{v}^2,\frac{3}{2}u{v}^2\right),\left(-3u^{2}v,u^{2}v\right),\left(uv,2vu\right)\text{ and }\left(4,-7\right)$ form the pair of similar polynomials.

Explanation of Solution

Given information: The given monomials are,

  $u{v}^2,-3u^{2}v,-u^3,\frac{3}{2}u{v}^2,uv,4,2vu,v^3,u^{2}v,-\mathrm{7....}\left(1\right)$

Calculation: The similar monomials are those which are identical in terms of variables but having different coefficients. Therefore from (1),

  $\begin{array}{c}u{v}^2,\frac{3}{2}u{v}^2\mathrm{......}\left(\text{Similar}\right)\\ -3u^{2}v,u^{2}v\mathrm{......}\left(\text{Similar}\right)\\ uv,2vu\mathrm{......}\left(\text{Similar}\right)\\ 4,-\mathrm{7......}\left(\text{Similar}\right)\end{array}$