Ex.9.1 Q1 Algebraic Expressions and Identities - NCERT Maths Class 8

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Question

Identify the terms, their coefficients for each of the following expressions.

(i) \(\quad 5xy{z^2} - 3zy\)

(ii) \(\quad 1 + x + {x^2}\)

(iii) \(\quad 4{x^2}{y^2} - 4{x^2}{y^2}{z^2} + {z^2}\)

(iv) \(\quad 3 - pq + qr - rp\)

(v) \(\begin{align}\quad \frac{x}{2} + \frac{y}{2} - xy\end{align}\)

(vi) \(\quad 0.3a - 0.6ab + 0.5b\)

Text Solution

What is known?

Expressions

What is unknown?

Terms and their coefficients

Reasoning:

The numerical factor of a term is called its numerical coefficient or simply coefficient.

Steps:

The terms and the respective coefficients of the given expressions are as follows.

 

-

Terms

Coefficients

(i)

\[\begin{align}&{{5}}xy{z^{\rm{2}}}\\&{{ -3}}zy\end{align}\] \(\begin{align}5\\- 3\end{align}\)

(ii)

\(\begin{align}&1\\&x\\&{x^2}\end{align}\) \(\begin{align}&1\\&1\\&1\end{align}\)

(iii)

\(\begin{align}&4{x^2}{y^2}\\- &4{x^2}{y^2}{z^2}\\&{z^2}\end{align}\) \(\begin{align}&4\\-& 4\\&1\end{align}\)

(iv)

\(\begin{align}&{3}\\ - &pq\\&qr\\ - &rp\end{align}\) \(\begin{align}&3\\- &1\\&1\\- &1\end{align}\)

(v)

\(\begin{align}&\frac{x}{2}\\&\frac{y}{2}\\- &xy\end{align}\) \(\begin{align}&\frac{1}{2}\\&\frac{1}{2}\\- &1\end{align}\)

(vi)

\(\begin{align}&0.3a\\- &0.6ab\\&0.5b\end{align}\)

\(\begin{align}&0.3\\- &0.6\\&0.5\end{align}\)

 

  
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