# 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 :

(a2 + ab + b2)(a - b)
Use a distributive property.
= a2(a - b) + ab( a - b) + b2(a - b)
= a2. a - a2. b + ab. a - ab. b + b2 . a - b2 . b
= a3 - a2b + a2b- ab2 + ab2 - b3 [ Add like terms]
= a3 -b3

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

Solution :

(1 - 4x)( 1 + x + x2)
= 1( 1 + x + x2 ) - 4x ( 1 + x + x2)
= 1 + 1.x + 1.x2 - 4x .1 - 4x.x - 4x.x2
= 1 + x + x2 - 4x - 4x2 - 4x3[ Bring the like terms together]
= 1 + x - 4x + x2 - 4x2 - 4x3
= 1 - 3x -3x2 - 4x3 [ Add like terms]
= - 4x3 - 3x2 -3x + 1 [ arranging in descending order of exponents]

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

Solution :

(a2 - b2) ( 4a3 - b3)
= a2(4a3 - b3)- b2(4a3 - b3)
= 4a5 - a2b3 - 4a3b2 + b5
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