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

● 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

Algebra Page

6th Grade Page

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