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
-
Basic Multiplication Facts | Repeated Addition |Multiplication Process
Jan 15, 25 12:23 AM
Some basic multiplication facts are needed to follow for multiplying numbers. The repeated addition of the same number is expressed by multiplication in short. -
Properties of Multiplication | Multiplicative Identity | Whole Numbers
Jan 15, 25 12:08 AM
There are six properties of multiplication of whole numbers that will help to solve the problems easily. The six properties of multiplication are Closure Property, Commutative Property, Zero Property… -
Multiplication Table | Learn Tables from 0 – 25 | Multiplication Table
Jan 14, 25 11:53 PM
In math multiplication table we will learn the tables from 0 – 25. These multiplication tables help the students to learn the essential multiplication facts. Multiplication tables are very important f… -
3rd Grade Math Worksheets |3rd Grade Math Sheets|3rd Grade Math Lesson
Jan 14, 25 11:02 PM
3rd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. Teachers and parents can also follow the worksheets to guide the students. -
3rd Grade Subtraction Worksheet | 3-Digit Subtraction Worksheets | Ans
Jan 14, 25 01:57 PM
In 3th Grade Addition Worksheet we will solve how to subtract 3-digit numbers by expansion, subtraction of 3-digit numbers without regrouping, subtraction of 3-digit numbers with regrouping, propertie…
● 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
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.