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.)