Multiplication of Algebraic Terms

A mathematical operation of multiplying two or more algebraic terms is called the multiplication of algebraic terms.

Introduction

Two or more algebraic terms are connected by a multiplication sign ($\times$) to get product of them. Due to the classification of the algebraic terms, there are two special cases for multiplying the algebraic terms in algebraic mathematics and it is essential to learn both the cases to multiply any two or more algebraic terms.

Required knowledge

Learn the following three mathematical concepts firstly to understand the multiplication of algebraic terms.

1. Exponents or Indices
2. Product Rules of Exponents
3. Power Rule of Exponents

Now, let’s start learning the different cases of multiplying the algebraic terms in algebra.

Multiplying the Like terms

The multiplication of two or more like algebraic terms can be done directly due to their similarly. As we know that the like algebraic terms have the same literal coefficient. Hence, the product of them is equal to the product of product of their numerical coefficients and their literal coefficient raised to the power of total number of like terms.

Examples

$(1) \,\,\,$ $2a \times 3a = 6a^2$

$(2) \,\,\,$ $h \times 3h \times 5h = 15h^3$

$(3) \,\,\,$ $(-4x^2y) \times 9x^2y = -36x^4y^2$

Multiplying the Unlike terms

The multiplication of two or more unlike algebraic terms can also be done directly even though they are dissimilar. In fact, the unlike algebraic terms have different literal coefficients. However, the product of them is calculated by the product of product of their numerical coefficients and product of their literal coefficients.

In this case, the product of literal coefficients are simply written by displaying all of them one after one in a row after writing the product of numerical coefficients of unlike terms. In some cases, the different literal coefficients of them may also have factors with one or more same literals and they are written as a factor due to same base.

$(1) \,\,\,$ $a \times b = ab$

$(2) \,\,\,$ $j \times (-5j^2k) \times 7k^2 = -35j^3k^3$

$(3) \,\,\,$ $(-4xy) \times 9x^2y \times 2xy^2= -72x^4y^4$

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