Class 7 Maths Algebraic Expressions | Terms of an Expression |

__Terms of an Expression__

Terms are added to form an expression.

Ex: terms 3x and 7 are added to form the expression 3x + 7

Again, the expression 2y^{2} – 7xy are formed by adding the terms

2y^{2} and -7xy i.e. 2y^{2} + (-7xy) = 2y^{2} – 7xy

**Factors of a term**

A term is a product of its factors.

Let us take a term 2y^{2}

The term 2y^{2} is a product of 2, y and y. Now, we say that 2, y and y are the factors of the term 2y^{2}

Again the term – 7xy is a product of the factors -7, x and y.

**Coefficient**

The numerical factor is said to be the numerical coefficient or simply the coefficient of the term.

Ex: In the term 20y^{2}, 20 is the coefficient of y^{2}.

Again, in the term -3xyz, -3 is the coefficient of xyz.

In general, a coefficient may be either a numerical factor or an algebraic factor or a product of two or

more factors.

Ex: In the term 7xy, 7 is the coefficient of xy, x is the coefficient of 7y and y is the coefficient of 7x.

In 5xy^{2}, 5 is the coefficient of xy^{2}, x is the coefficient of 5y^{2} and y^{2} is the coefficient of 5x.

We can represent the terms and factors of an expression in an efficient way by using a tree diagram.

Ex: Let us take the expressions 3xy – 10x, 5x^{3} – 2xy to draw the tree.

__Problem:__ Identify terms which contain x and give the coefficient of x.

(i) y^{2} x + y (ii) 13y^{2} – 8xy (iii) x + y + 2 (iv) 5 + z + zx (v) 1 + x + xy

(vi) 12xy^{2} + 25 (vii) 7x + xy^{2}

Solution:

.