# Multiplication of Polynomial by Binomial

In this section we will discuss Multiplication of Polynomial by Binomial.

Here also we will use a distributive property. Examples :

1) (a2 + ab + b2)(a - b)

Solution :

(a
2 + ab + b 2 )(a - b)
Use a distributive property.
= a
2 (a - b) + ab( a - b) + b 2 (a - b)
= a
2 . a - a 2 . b + ab . a - ab . b + b 2 . a - b 2 . b
= a
3 - a2b + a2b - ab2 + ab2 - b 3 [ Add like terms]
= a
3 -b 3

2) (1 - 4x)( 1 + x + x2)

Solution :

(1 - 4x)( 1 + x + x
2 )
= 1( 1 + x + x
2 ) - 4x ( 1 + x + x 2 )
= 1 + 1.x + 1.x
2 - 4x .1 - 4x.x - 4x.x 2
= 1 + x + x
2 - 4x - 4x 2 - 4x 3 [ Bring the like terms together]
= 1 + x - 4x + x
2 - 4x 2 - 4x 3
= 1 - 3x -3x
2 - 4x 3 [ Add like terms]
= - 4x
3 - 3x 2 -3x + 1 [ arranging in descending order of exponents]

3) (a2 - b2) ( 4a3 - b3)

Solution :

(a
2 - b 2 ) ( 4a 3 - b 3 )
= a
2 (4a 3 - b 3 )- b 2 (4a 3 - b 3 )
= 4a
5 - a 2 b 3 - 4a 3 b 2 + b 5
Multiplication of algebraic expressions

Multiplication of Monomial by Binomial
Multiplication of Binomial by Binomial
Multiplication of Polynomial by Monomial
Multiplication of Polynomial by Binomial

Algebraic Expressions page