# Multiplication of Polynomial by monomial

Multiplication of Polynomial by Monomial, use the following steps :

1) Use a distributive law to multiply polynomial by monomial.
2) Multiply each term of the parenthesis by monomial. Some more examples :

1) -3ab ( a3b + a2b2 - ab)

Solution :

= (-3ab
. a 3 b) + (-3ab . a 2 b 2 ) + ( -3ab . -ab)

= -3a
1+3 b 1+1 - 3a 1+2 b 1+2 + 3a 1+1 b 1+1

= -3a
4 b 2 - 3a 3 b 3 + 3a 2 b 2

2) 3( 5 - 2d - d2)

Solution :

= (3 x 5) - (3 x 2d ) - (3 x d
2 )

= 15 - 6d - 3d
2

3) -5a ( a3 - 2a2 + 7a + 8)

Solution :

= ( -5a x a
3 ) + ( -5a x 2a 2 ) + ( -5a x 7a) + (-5a x 8)

= -5a
4 - 10a 3 - 35a 2 - 40a

4) 0(x4 + x3 + x2 + x + 1)

Solution :

Any polynomial multiply by zero is zero.

So, 0
. (x 4 + x 3 + x 2 + x + 1) = 0

5) 1 ( x4 - 7 )

Solution :

Any polynomial multiply by 1 is the polynomial itself.
So, 1
. ( x 4 - 7 ) = ( x 4 - 7 )

6) 2a/3(a
3 + 6a 2 + 12)

Solution :
= ( 2a/3 x a
3 ) + ( 2a/3 x 6a 2 ) + ( 2a/3 x 12)

= 2a
4 /3 + 4a 2 + 8a
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