# Multiplication of Monomial by Binomial

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**For solving this multiplication use the following steps:**

1) Monomial is outside the parenthesis (bracket).

2) Binomial is inside the parenthesis.

3) Use a distributive property to open the parenthesis.

4) Distributive property ---> Multiply each term of the parenthesis by the monomial keeping the addition or subtraction sign same.

**Examples :**

1) Multiply : 3x(x + 4)

**Solution :**

As 3x is outside the parenthesis, multiply x and 4 by 3x

3x(x + 4) = 3x

**.**x + 3x

**.**4

= 3x

^{1 + 1}+ 12x

= 3x

^{2}+ 12x

2) Multiply : 4x

^{2}y

^{3}(3x

^{2}y

^{2}- 2xy)

**Solution :**

4x

^{2}y

^{3}(3x

^{2}y

^{2}- 2xy)

= 4x

^{2}y

^{3}

**.**3x

^{2}y

^{2}- 4x

^{2}y

^{3}

**.**2xy

= 12x

^{4}y

^{5}- 8x

^{3}y

^{4}

3) Multiply : -2xy (x

^{2}y - 4x)

**Solution :**

-2xy (x

^{2}y - 4x)

= -2xy

**.**x

^{2}+ 2xy

**.**4x

= -2x

^{3}y

^{2}+ 8x

^{2}y

4) Multiply : 3ab(a

^{2}b - ab

^{2})

**Solution :**

3ab(a

^{2}b - ab

^{2})

= 3ab

**.**a

^{2}b - 3ab

**.**ab

^{2}

= 3a

^{3}b

^{2}- 3a

^{2}b

^{3}

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**Practice**

1) -4ab(2a

^{2}+ 5ab)

2) 3x(4y

^{2}- x

^{3})

3) -2(a

^{2}+ 2b

^{2})

4) 2/3(6x

^{2}+ 9y)

5) -1/2(12x

^{2}- 18y

^{2})

**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**

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