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)

Right Option : A
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Explanation
Question : 2

Simplify:

(x-3a) (x-2b)

Right Option : D
View Explanation
Explanation
Question : 3

Multiply: (2.5x +1.2y) by (0.6x - 0.5y)

Right Option : C
View Explanation
Explanation
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