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, m^{2 + 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

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● Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

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Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials

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