# 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 ( a**

^{3}b + a^{2}b^{2}- 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 - d**

^{2})**Solution :**

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

^{2})

= 15 - 6d - 3d

^{2}

**3) -5a ( a**

^{3}- 2a^{2}+ 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(x**

^{4}+ x^{3}+ x^{2}+ x + 1)**Solution :**

Any polynomial multiply by zero is zero.

So, 0

**.**(x

^{4}+ x

^{3}+ x

^{2}+ x + 1) = 0

**5) 1 ( x**

^{4}- 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

• Multiplication of Monomial by Binomial

• Multiplication of Binomial by Binomial

• Multiplication of Polynomial by Monomial

• Multiplication of Polynomial by Binomial

**Algebraic Expressions page**