# Multiplication of Algebraic Expressions

In Multiplication of Algebraic Expressions, we use the laws of exponents.There are different types of multiplication.

1) Monomial by monomial

2) Monomial by Binomial

3) Polynomial by monomial

4) Trinomial by monomial

5) Trinomial by trinomial

**Steps used in multiplication of monomial by monomial**

1) Write the two numbers with multiplication sign (x) between them or put a dot. The dot considered as multiplication.

2) Multiply the numbers.

3) If the bases are same then add the exponents.

**Examples :**

1)Multiply y

^{3}and y

^{-4}

**Solution :**

= y

^{3}. y

^{-4}

= y

^{3+(-4)}

= y

^{-1}

2) Find the product of p

^{2 }and p

^{5}

**Solution :**

= p

^{2 }. p

^{5}

= p

^{2+5}

= p

^{7}

3) Find the product of 3ab and 4a

^{2}b

**Solution :**

= 3ab x 4a

^{2}b

= (3 x 4) x a x a

^{2}b x b

= 12 a

^{1 +2 }b

^{1 +1}

= 12 a

^{3}b

^{2}

4) Multiply : 8p

^{3}q

^{5}x 4

**Solution :**

= p

^{4}q

^{3}

= (8 x 4) x p

^{ 3+4}x q

^{5+3}

= 32 p

^{7}q

^{8}

**Monomial by Binomial**

5) Multiply : 4abc and 5a

^{2}b

^{-3}c

^{6}

**Solution :**

= 4abc . 5a

^{2}b

^{-3}c

^{6}

= ( 4 x 5)(abc x a

^{2}b

^{-3}c

^{6})

= 20 a

^{1+ 2}x b

^{1 + (-3)}x c

^{1 + 6}

= 20 a

^{3}b

^{(-2)}c

^{7}

= 20 a

^{3}c

^{7}/ b

^{2}[ Make the exponent of 'b' positive]

**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

**Multiplication of expressions to Algebraic Expressions page**