# CLASS-8HORIZONTAl MULTIPLICATION OF POLYNOMIAL BY MONOMIAL OF ALGEBRAIC EXPRESSION

Horizontal Multiplication of a Polynomial by a Monomial -

To find the product of a polynomial and a monomial, multiply each term of the polynomial by the monomial and add the products.

Thus, the law is a X ( b + c + d + e + ……… )

= (a X b) + (a X c ) + (a X d) + (a X e) + …………… [distributive law]

Or, alternatively ( b + c + d + e + ……… ) X a

=  (b X a) + (c X a ) + (d X a) + (e X a) + …………… [distributive law]

There are some example are given below, for your understanding –

Horizontal Method of Multiplication of Algebraic Expression -

Example.1)  Multiply 5x – 3xy + 8 by 5

Ans.) As per the given condition -

( 5x – 3xy + 8 ) X 5 =  (5 X 5) x (–) (3 X 5) xy + (8 X 5)                                                                                                                             = 25x – 15xy + 40          (Ans.)

Example.2) Multiply 2x² + 8yᶟ + 7xy – 4xy² with 5x²y²

Ans.) As per the given condition -

(2x² + 8yᶟ + 7xy – 4xy²) X (5x²y²)

=  2x². 5x²y²+ 8yᶟ. 5x²y²+ 7xy. 5x²y²- 4xy².5x²y²

= (2x5). x²⁺².y²+ (8X5).x².yᶟ⁺²+ (7X5).x¹⁺². y¹⁺²- (4X5).x¹⁺². y²⁺²

=  10x⁴y² + 40x²y⁵ + 35xᶟyᶟ - 20xᶟy⁴            (Ans.)