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 y³ and y^-4

Solution :
= y³ . y^-4
= y^3+(-4)
= y^-1


2) Find the product of p² and p⁵

Solution :
= p² . p⁵
= p²⁺⁵
= p⁷

3) Find the product of 3ab and 4a²b

Solution :
= 3ab x 4a²b
= (3 x 4) x a x a²b x b
= 12 a^{1 +2} b^{1 +1}
= 12 a³b²

4) Multiply : 8p³q⁵ x 4

Solution :
= p⁴q³
= (8 x 4) x p ³⁺⁴x q⁵⁺³
= 32 p⁷q⁸

Monomial by Binomial

5) Multiply : 4abc and 5a²b^-3c⁶

Solution :
= 4abc . 5a²b^-3c⁶

= ( 4 x 5)(abc x a²b^-3c⁶)

= 20 a^{1+ 2}x b^{1 + (-3)} x c^{1 + 6}

= 20 a³b^(-2)c⁷

= 20 a³c⁷/ b²[ Make the exponent of 'b' positive]

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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 expressions to Algebraic Expressions page

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