A mathematical operation of multiplying an algebraic term by its unlike term is called the multiplication of unlike algebraic terms.

In mathematics, two or more unlike algebraic terms are often engaged in multiplication to represent a quantity by the product of them. Hence, it is very important to understand how to multiply two or more unlike algebraic terms.

The product of the two or more unlike algebraic terms is equal to the product of the product of numerical factors and the product of literal factors. In this case, the product of literal factors can be exponential form and it is possible when the literal factors contain at least a literal commonly.

$3xy$ and $4y^2z$ are two unlike algebraic terms and the multiplication of them is written as follows in mathematics.

$3xy \times 4y^2z$

Remember, the knowledge on exponents is required to understand the multiplication of unlike algebraic terms clearly.

01

Factorize each algebraic term as numerical and basic literal factors firstly. After that, write the like factors closely in the multiplication.

$3xy \times 4y^2z$ $\,=\,$ $3 \times x \times y \times 4 \times y^2 \times z$

$\implies 3xy \times 4y^2z$ $\,=\,$ $3 \times 4 \times x \times y \times y^2 \times z$

$\implies 3xy \times 4y^2z$ $\,=\,$ $(3 \times 4) \times x \times (y \times y^2) \times z$

02

Multiply the numbers and also express the product of like factors in exponential form.

$\implies 3xy \times 4y^2z$ $\,=\,$ $12 \times x \times y^3 \times z$

03

Now, combine the all factors to form an algebraic term and it represents the product of them.

$\,\,\, \therefore \,\,\,\,\,\, 3xy \times 4y^2z$ $\,=\,$ $12xy^3z$

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