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

The like algebraic terms participate in multiplication to represent a quantity by their product. So, it is essential for everyone to know how to multiply two or more like algebraic terms in mathematics.

In fact, the like algebraic terms contain same literal factors. Therefore, the product of the multiplication of two or more like algebraic terms is equal to the product of the numerical factors of the terms and the whole power of the literal factor, where the whole power is equal to the number of like terms participated in the multiplication.

$4xy^2$ and $7xy^2$ are two like algebraic terms and the multiplication of them is expressed in mathematics as follows.

$4xy^2 \times 7xy^2$

The product of multiplication of two or more like algebraic terms can be obtained in two different methods.

01

It is a recommendable method for those who learn algebra newly.

Firstly, factorise each algebraic term as numerical and basic literal factors and then, group the like factors.

$4xy^2 \times 7xy^2$ $\,=\,$ $4 \times x \times y^2 \times 7 \times x \times y^2$

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $4 \times 7 \times x \times x \times y^2 \times y^2$

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $(4 \times 7) \times (x \times x) \times (y^2 \times y^2)$

Multiply the numbers directly and express like factors in exponential form to represent their product.

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $28 \times x^2 \times {(y^2)}^2$

Use, power of a power law to simplify it further.

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $28 \times x^2 \times y^4$

Express the product of the factors as an algebraic term.

$\,\,\, \therefore \,\,\,\,\,\, 4xy^2 \times 7xy^2$ $\,=\,$ $28x^2y^4$

02

It is a recommendable method for those who have good knowledge on exponents.

Split the like terms in terms of numerical factors and literal factors, and then group them.

$4xy^2 \times 7xy^2$ $\,=\,$ $4 \times xy^2 \times 7 \times xy^2$

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $4 \times 7 \times xy^2 \times xy^2$

Get the product of both like factors and express them in simplified form.

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $(4 \times 7) \times (xy^2 \times xy^2)$

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $28 \times {(xy^2)}^2$

$\implies 4xy^2 \times 7xy^2$ $\,=\,$ $28 \times x^2y^4$

Now, combine the factors as an algebraic term to represent product of them.

$\,\,\, \therefore \,\,\,\,\,\, 4xy^2 \times 7xy^2$ $\,=\,$ $28x^2y^4$

Thus, you can multiply either two or more like algebraic terms in any one of the above two methods to get the product of the mathematically.