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

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

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

Question : 3

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

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Multiplication of Binomials

Multiplication of Binomials

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Aman Kumar Shrivastava

Cheshta

Manish Kumar

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Upmanyu Sharma

Om Umang

Ayan Ghosh

Aman Kumar Shrivastava

Hiya Gupta

Sharandeep Singh

Barkha Arora

Shreya Shrivastava

Yatharthi Sharma

Anika Saxena

Archit Segal

Manya

Barkha Arora

Yogansh Nyasi

Aman Kumar Shrivastava

Manish Kumar