 # Identify the terms, their coefficients for each of the following expressions: `
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) $\frac{a}{2}+\frac{b}{2}-a b$

(vi) 0.2 0.3xy + 0.5y

Solution:

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: $27, x, x y z, \frac{1}{2} x^{2} y z$ etc.

The number factor of the term is called its coefficient.

(i) The expression $7 x^{2} y z-5 x y$ consists of two terms, i.e., $7 x^{2} y z$ and $-5 x y$.

The coefficient of $7 x^{2} y z$ is 7 and the coefficient of $-5 x y$ 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 $3 x^{2} y^{2}-5 x^{2} y^{2} z^{2}+z^{2}$ consists of three terms, i.e., $3 x^{2} y^{2},-5 x^{2} y^{2} z^{2}$ and $z^{2}$. The coefficient of $3 x^{2} y^{2}$ is 3 . The coefficient of $-5 x^{2} y^{2} z^{2}$ is $-5$ and the coefficient of $z^{2}$ is 1 .

(iv) The expression $9-a b+b c-c a$ consists of four terms $-9,-a b, b c$ and $-c a$. The coefficient of the term 9 is 9 . The coefficient of $-a b$ is $-1$. The coefficient of $b c$ is 1 , and the coefficient of $-c a$ is $-1$.

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

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