Question

Identify the terms, their coefficients for each of the following expressions:
(i) 7x²yz − 5xy
(ii) x² + x + 1
(iii) 3x²y² − 5x²y²z² + z²
(iv) 9 − ab + bc − ca
(v) $\frac{a}{2}+\frac{b}{2}-ab$
(vi) 0.2x − 0.3xy + 0.5y

Answer 1

Definitions:

A term in an algebraic expression can be a constant, a variable or a product of constants and variables separated by the signs of addition (+) or subtraction ($-$) . Examples: 27, x, xyz, $\frac{1}{2}{x}^{2}yz$ etc.
The number factor of the term is called its coefficient.

(i) The expression $7x^{2}yz-5xy$ consists of two terms, i.e., $7x^{2}yz$ and $-5xy$.
The coefficient of $7x^{2}yz$ is 7 and the coefficient of $-5xy$ is $-5$.

(ii) The expression $x^2+x+1$ consists of three terms , i.e.,​ $x^2$, x and 1.
The coefficient of each term is 1.

(iii) The expression $3x^2{y}^2-5x^2{y}^2{z}^2+z^2$ consists of three terms , i.e.,​ $3x^2{y}^2$, $-5x^2{y}^2{z}^2$ and $z^2$. The coefficient of $3x^2{y}^2$ is 3. The coefficient of $-5x^2{y}^2{z}^2$ is $-5$ and the coefficient of $z^2$ is 1.
(iv) The expression $9-ab+bc-ca$ consists of four terms — $9,-ab,bc\text{and}-ca$. The coefficient of the term 9 is 9. The coefficient of $-ab$ is $-$1. The coefficient of $bc$ is 1, and the coefficient of $-ca$ is $-$1.

(v) The expression $\frac{a}{2}+\frac{b}{2}-ab$ consists of three terms , i.e.,​ $\frac{a}{2},\frac{b}{2}\text{and}-ab$. The coefficient of $\frac{a}{2}$ is $\frac{1}{2}$. The coefficient of $\frac{b}{2}$ is $\frac{1}{2}$, and the coefficient of $-ab$ is $-$1.

(vi) The expression $0.2x-0.3xy+0.5y$consists of three terms , i.e.,​ $0.2x,-0.3xy\text{and}0.5y.$ The coefficient of $0.2x$ is $0.2$. The coefficient of $-0.3xy$ is $-0.3$, and the coefficient of $0.5y$ is $0.5$.