# Multiplication of Two Monomials

Multiplication of two monomials means product of their numerical coefficients and product of their literal coefficients.

According to the power of literal quantities we can express, m2 = m × m and m3 = m × m × m. Here, m2 and m3 both are monomials.

Therefore, multiplication of m2 and m3 = m2 × m3

= (m × m) × (m × m × m)

= m × m × m × m × m

= m5

Or, in other way we can simply add the powers since the base is same. In case of m2 × m3 both have same base then we get, m2 + 3 = m5

Note: To multiply, the powers of like factors or same base are added.

Similarly, we can multiply the two monomials 7a2b and 5ab2 in two different ways.

7a2b and 5ab2

= 7a2b × 5ab2

= (7 × a × a × b) × (5 × a × b × b)

= (7 × 5) × (a × a × a) × (b × b × b)

= 35a3b3

or, in other way we can simply 7a2b × 5ab2

= (7 × 5) ∙ a2 + 1 ∙ b1 + 2

= 35a3b3

Therefore, to multiply two monomials, multiply their coefficients together and prefix their product to the product of letters in the monomials.

Examples on multiplication of two monomials:

1. Find the product of 9a2b3, 2b2c5 and 3ac2.

9a2b3 × 2b2c5 × 3ac2

= (9 × a × a × b × b × b) × (2 × b × b × c × c × c × c × c) × (3 × a × c × c)

= (9 × 2 × 3) × (a × a × a) × (b × b × b × b × b) × (c × c × c × c × c × c × c)

= 54 × a3 × b5 × c7

= 54a3b5c7

2. Find the product of -9x2yz3, 5/3xy3z2 and -7yz.

-9x2yz3 × 5/3xy3z2 × -7yz

= (-9 × 5/3 × -7) × (x2 × x) × (y × y3 × y) × (z3 × z2 × z)

Now we need to add the powers of the same bases i.e. x, y and z.

= (315/3) × (x2 + 1) × (y1 + 3 + 1) × (z3 + 2 + 1)

= 105 × x3 × y5 × z6

= 105x3y5z6

Types of Algebraic Expressions

Degree of a Polynomial

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials

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