# Multiplication of Algebraic Expressions

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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**

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