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

The product of $(x^2+3x+5): : and : : (x^2-1)$ is
A. $x^4+3x^3-4x^2-3x+5$		B. $x^4+3x^3+4x^2-3x-5$
C. $x^4+3x^3+4x^2+3x-5$		D. $x^4+3x^3-4x^2-3x-5$
Right Option : B
View Explanation

Question : 2

Find the product of $large (2x+4y)(3x-2y)$
A. $x^2-8xy-8y^2$		B. $8x^2-xy-8y^2$
C. $6x^2+8xy-8y^2$		D. $8x^2+8y^2-8xy+8$
Right Option : C
View Explanation

Question : 3

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

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Multiplication of Binomials

Multiplication of Binomials

Students / Parents Reviews [10]

Om Umang

Barkha Arora

Shreya Shrivastava

Prisha Gupta

Manish Kumar

Archit Segal

Eshan Arora

Shivam Rana

Cheshta

Hiya Gupta