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Multiplication of Binomials

Polynomial I - Concepts

Like and Unlike Terms

Finding Value of an Expression

Polynomial Expression

Degree of a Term

Degree of a Polynomial

Standard Form For a Polynomial

Multiplication of Binomials

Division of Polynomial by a Monomial

Factor And Remainder Theorem

Multiplication of Polynomials

Class - 9th IMO Subjects

Concept Explanation

Multiplication of Binomials

Binomial expression are those expression which have two terms, and the multiplication can be done by multiplying first term with both the terms of the second expression and then multiplying the second term with both the terms of the second expression. Consider two binomials. say (a+b) and (c+d). and by using the distributive property of multiplication of literals over their addition, we have

$large ( a + b ) times ( c + d ) = a times ( c + d ) + b times ( c + d )$

$large = ( a times c;+; a;times d) +(b ;times c ;+;b ;times d )$

$large = ac;+;ad ;+bc ;+bd$

Illustration: Multiply (3x+2y) and (5x + 3y)

Solution: The multiplication can be done as follows

$(3x ;+;2y) times (5x;+;3y)$

$= 3x times (5x ;+;3y) + 2y; times ;(5x;+;3y)$

$= (3x;times;5x ;+;3x;times 3y ) ;+;(2y;times 5x;+;2y;times 3y)$

$= (15x^{2};+;9xy);+;(10xy;+;6y^{2})$

$= 15x^{2};+;9xy;+10xy;+;6y^{2}$

$= 15x^{2};+;19xy;+;6y^{2}$

Illustration: Multiply (2x + 3y) and ( 4x - 5y)

Solution: The multiplication can be done as follows

$(2x;+;3y);times;(4x;-;5y)$

$= 2x;times (4x;-;5y);+;3y;times;(4x;-;5y)$

$= (2x;times;4x;-;2x;times;5y);+;(3y;times;4x;-;3y;times;5y)$

$= (8x^{2};-;10xy);+;(12xy;-;15y^{2})$

$= 8x^{2};-;10xy;+;12xy;-;15y^{2}$

$= 8x^{2};+;2xy;-;15y^{2}$

$= 8x^{2};-;10xy;+;12xy;-;15y^{2}$

Illustration: $Multiply ;(3x^2+2y); and ;(5x + 3y^2)$

Solution: The multiplication can be done as follows

$(3x^2 ;+;2y) times (5x;+;3y^2)$

$= 3x^2 times (5x ;+;3y^2) + 2y; times ;(5x;+;3y^2)$

$= (3x^2;times;5x ;+;3x^2;times 3y^2 ) ;+;(2y;times 5x;+;2y;times 3y^2)$

$= (15x^{3};+;9x^2y^2);+;(10xy;+;6y^{3})$

$= 15x^{3};+;9x^2y^2;+10xy;+;6y^{3}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Expand: (2x-3)(x-1)
A. $large 2x^2-x-3$	B. $large 2x^2-x+3$	C. $large 2x^2-5x-3$	D. $large 2x^2-5x+3$
Right Option : D
View Explanation

Question : 2

Simplify each of the following: $2x(x^3-y^{3})-2y(y^3-x^{3})$
A. $2x^{4}-2y^{4}-2xy^{3}+2x^{3}y$	B. $2x^5+2x^2y-2y^3+2xy^2$	C. $2x^5-2x^2y+2x^2y+2xy^2$	D. $2x^5-2x^2y+2x^3y$
Right Option : A
View Explanation

Question : 3

Multiply (5x - 2y) by (5a - 2b)
A. 25xa - 10xb - 10ay + 4ya		B. 25xa - 10xb - 10ab + 4yb
C. 25xa - 10xb - 10ay + 4yb		D. 25xy - 10xb - 10ay + 4yb
Right Option : C
View Explanation

Chapters

Polynomials II

Direct and Inverse Variation

Linear Equations in One Variable

Introduction to Trigonometry

Introduction to Euclids Geometry

Herons Formula Complete

Polynomial I

Surface Area and Volume II

Surface Area and Volume I

Coordinate Geometry

Constructions

Areas Of Parallelograms And Triangles II

Areas Of Parallelograms And Triangles I

Linear Equations in Two Variables

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Multiplication of Binomials

Multiplication of Binomials

Students / Parents Reviews [10]

Hiya Gupta

Yatharthi Sharma

Eshan Arora

Prisha Gupta

Archit Segal

Aman Kumar Shrivastava

Shivam Rana

Manish Kumar

Ayan Ghosh

Om Umang