Expand and Simplify Polynomials - G...
Expand and Simplify Polynomials - Grade 9

Multiplication of Algebraic Expressions

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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
= y3+(-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 a1 +2 b1 +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 a1+ 2x b1 + (-3) x c1 + 6

= 20 a3b(-2)c7

= 20 a3c7/ b2[ 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 expressions to Algebraic Expressions page

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