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Multiplication of Binomials

Algebraic Expressions - Concepts

Framing an Algebraic Expression

Monomial Expression

Binomial Expression

Trinomial Expression

Like and Unlike Terms

Finding Value of an Expression

Addition of Algebraic Expression

Subtraction of Algebraic Expression

Multiplication of Monomials

Multiplication of Binomial with a Monomial

Multiplication of Binomials

Division of Polynomial by a Monomial

Degree of a Term

Degree of a Polynomial

Class - 9th Aus Edu Subjects

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

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

Question : 2

Multiply: $(2x-3y^2)$ $(2x^2+3y^2)$
A. $4x^3+6xy^2-6x^2y^2-9y^3$	B. $4x^3+6xy^2-6x^2y^2-9y^4$	C. $4x^3+6xy^2-6x^2y^2-6y^3$	D. None of these
Right Option : B
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

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Multiplication of Binomials

Multiplication of Binomials

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Students / Parents Reviews [10]

Archit Segal

Shreya Shrivastava

Shivam Rana

Manish Kumar

Hiya Gupta

Eshan Arora

Yatharthi Sharma

Ayan Ghosh

Barkha Arora

Aman Kumar Shrivastava

Multiply: $(2x-3y^2)$ $(2x^2+3y^2)$