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

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

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

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

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

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

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

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

Sample Questions

(More Questions for each concept available in Login)

Question : 1

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

Question : 2

Simplify: $(1.2a-3.5b)(15a^2+10b^2)$
A. $18a^3+12ab^2-52.5a^2b-35b^3$	B. $18a^3+12ab^2-52.5a^2b-45b^2$	C. $18a^2+12ab^3-52.5a^2b-35b^3$	D. None of these
Right Option : A
View Explanation

Question : 3

If $(3x-4)(5x+7)=15x^2-ax-28$ then a= _______________.
A. 1	B. -1	C. -2	D. none of these
Right Option : B
View Explanation

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Multiplication of Binomials

Multiplication of Binomials

Students / Parents Reviews [10]

Hiya Gupta

Shreya Shrivastava

Manish Kumar

Om Umang

Eshan Arora

Ayan Ghosh

Archit Segal

Prisha Gupta

Aman Kumar Shrivastava

Yatharthi Sharma