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Algebraic Expressions

    Factors of a term

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7th class > Algebraic Expressions > Factors of a term

Factors of a term

We saw above that the expression 4x2−3xy, consists of two terms 4x2 and −3xy. The term 4x2 is a product of 4, x and x; we say that 4, x and x are the factors of the term 4x2 A term is a product of its factors. The term −3xy is a product of the factors –3, x and y.

We can represent the terms and factors of the terms of an expression conveniently and elegantly by a tree diagram. The tree for the expression 4x2–3xy, is as shown in the adjacent figure.

Note, in the tree diagram, we have used dotted lines for factors and continuous lines for terms. This is to avoid mixing them.

Let us draw a tree diagram for the expression 5xy + 10.

The factors are such that they cannot be further factorised. Thus we do not write 5xy as 5 × xy, because xy can be further factorised. Similarly, if x3 were a term, it would be written as x × x × x and not x^2xx Also, remember that 1 is not taken as a separate factor.