Multiplication of Binomials

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

Simplify: $2x^2(x^3-y)-2y^2(y^3-x)$
A. $2x^5-2x^2y-2y^5+2xy^2$	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 : 2

Simplify: $(x-3a) (x-2b)$
A. $x^2-(3a+2b)x+ab$		B. $x^2+(3a-b)+2$ $x^2+(3a-b)+2$
C. $x^2-(x+2b)^2$		D. $(x^2 -(3a +2b)x + 6ab)$
Right Option : D
View Explanation

Question : 3

Multiply: (2.5x +1.2y) by (0.6x - 0.5y)
A. $1.5x^2-0.53xy-0.6y^4$	B. $2.5x^2-0.53xy-0.6y^2$	C. $1.5x^2-0.53xy-0.6y^2$	D. None of these
Right Option : C
View Explanation

Chapters

Permutation and Combination

Problems On Boats And Stream

Rules For Divisibility

Number Theory

HCF And LCM

Cube and Cube Roots

Square and Square Root

Partnership and Mixture

Time, Speed and Distance

Surface Area and Volume

Algebraic Identities

Polynomial

Quadratic Equations

Simple and Compound Interest

Profit Loss and Discount

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Multiplication of Binomials

Multiplication of Binomials

Students / Parents Reviews [10]

Manish Kumar

Om Umang

Hiya Gupta

Cheshta

Yatharthi Sharma

Prisha Gupta

Aman Kumar Shrivastava

Shivam Rana

Shreya Shrivastava

Eshan Arora