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 + 30xzSolved 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
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
Algebra Page
6th Grade Page
From Multiplication of Polynomial by Monomial to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
What are Parallel Lines in Geometry? | Two Parallel Lines | Examples
Apr 19, 24 04:39 PM
In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other -
Perpendicular Lines | What are Perpendicular Lines in Geometry?|Symbol
Apr 19, 24 04:01 PM
In perpendicular lines when two intersecting lines a and b are said to be perpendicular to each other if one of the angles formed by them is a right angle. In other words, Set Square Set Square If two… -
Fundamental Geometrical Concepts | Point | Line | Properties of Lines
Apr 19, 24 01:50 PM
The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples. -
What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral
Apr 19, 24 01:22 PM
What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments. -
Simple Closed Curves | Types of Closed Curves | Collection of Curves
Apr 18, 24 01:36 AM
In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.
● Terms of an Algebraic Expression - Worksheet
Worksheet on Types of Algebraic Expressions
Worksheet on Degree of a Polynomial
Worksheet on Addition of Polynomials
Worksheet on Subtraction of Polynomials
Worksheet on Addition and Subtraction of Polynomials
Worksheet on Adding and Subtracting Polynomials
Worksheet on Multiplying Monomials
Worksheet on Multiplying Monomial and Binomial
Worksheet on Multiplying Monomial and Polynomial