# 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) (a**

^{2}+ ab + b^{2})(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}- a

^{2}b + a

^{2}b - ab

^{2}+ ab

^{2}- b

^{3}[ Add like terms]

= a

^{3}-b

^{3}

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

^{2})**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) (a**

^{2}- b^{2}) ( 4a^{3}- b^{3})**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

• Multiplication of Monomial by Binomial

• Multiplication of Binomial by Binomial

• Multiplication of Polynomial by Monomial

• Multiplication of Polynomial by Binomial

**Algebraic Expressions page**