Multiplying Monomials

Multiplying monomials is a method of simplifying them by finding the product of their coefficients followed by the product of their variables.

For example, the product of two monomials, 5m and 7n, is:

5m ✕ 7n = (5 ✕ 7) ✕ (m ✕ n) = 35mn

Here, we observe that the product of monomials gives a monomial. Also, we usually write the variables in alphabetical order while writing the product. 

Now, let us multiply another two monomials, 2p and 3p⁵.

On multiplying the coefficients, we get 

(2 ✕ 3) = 6

On multiplying the variables, we get 

(p ✕ p⁵), where both the variables have the same base and different exponents.

By applying the exponent rules (a^m ✕ aⁿ = a^m+n), we get

p¹⁺⁵ = p⁶

Thus, the product is 6p⁶.

With Three or More Monomials

To find the product of more than two monomials, we calculate the product of the first two monomials and then multiply it with the next monomial, and the process continues.

Let us multiply 3r⁴s³t, 2rs, and 5s²t³.

Now, on multiplying the coefficients, we get

(3 ✕ 2 ✕ 5) = 30

On multiplying the variables, we get

(r⁴s³t ✕ rs ✕ s²t³) = (r⁴ ✕ r) ✕ (s³ ✕ s ✕ s²) ✕ (t ✕ t³) = r¹⁺⁴s³⁺¹⁺²t¹⁺³

Thus, the product is r⁵s⁶t⁴.