Multiplication of Polynomial by Monomial

Multiplication of polynomial by monomial means every terms of the polynomial are multiplied by the monomial.

Multiplication of 3a²b – 5ab² + 4ab and 2ab

First we will write the monomial (2ab) and the polynomial (3a²b – 5ab² + 4ab) in the same row and then separate it by using the multiplication sign.

= 2ab × (3a²b – 5ab² + 4ab)

Now we will multiply each term of the polynomial (3a²b – 5ab² + 4ab) by the monomial (2ab)

= (2ab × 3a²b) – (2ab × 5ab²) + (2ab × 4ab)

= 6a³b² – 10a²b³ + 8a²b²

Similarly, to find the product of 3x + 5y – 6z and - 5x

First we will write the monomial (5x) and the in the polynomial (3x + 5y – 6z) same row and then separate it by using the multiplication sign.

= -5x × (3x + 5y – 6z)

Now we will multiply each term of the polynomial (3x + 5y – 6z) by the monomial (-5x)

= (-5x × 3x) + (-5x × 5y) – (-5x × 6z)

= -15x² – 25xy + 30xz

Solved examples on multiplication of polynomial and monomial:

1. Find the product of x – y - z and -8x².

= -8x² × (x – y – z)

= (-8x² × x) – (-8x² × y) – (-8x² × z)

= -8x³ + 8x²y + 8x²z



2. Find the product of 5abc – 6a²bc – 6ab²c and 3abc².

= 3abc² × (5abc – 6a²bc – 6ab²c)

= (3abc² × 5abc) – (3abc² × 6a^2bc) – (3abc² × 6ab²c)

= 15a²b²c³ - 18a³b²c³ - 18a²b³c³



3. Find the product of x² + 2xy + y² + 1 by z.

= z × (x² + 2xy + y² + 1)

= (z × x²) + (z × 2xy) + (z × y²) + (z × 1)

= x²z + 2xyz + y²z + z



4. Find the product of 4p³ – 12pq + 9q² and -3pq.

= -3pq × (4p³ – 12pq + 9q²)

= (-3pq × 4p³) - (-3pq × 12pq) + (-3pq × 9q²)

= -12p⁴q + 36p²q² – 27pq³

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● Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

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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