# 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

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