Horizontal Multiplication of two Polynomial –
To find the product of two polynomials, multiply all the terms of one polynomial by each of the terms of the other polynomial and add the resulting products.
Now we will show you some more example for your better understanding –
Horizontal Method of Multiplication of Algebraic Expression -
Example.1) Find the product of (3x+5y) by (2a – 7b)
Ans.) We first multiply each term of (3x+5y) by 2a, then multiply each term of (3x+5y) by (- 7b). finally, we add all the term –
Thus, (3x+5y) X (2a – 7b) = 3x. 2a + 5y.2a – 3x.7b – 5y.7b
= 6xa + 10ya – 21xb – 35yb (Ans.)
Example.2) Find the product of (5x+3y – 4z ) by (3xy – 7yz + 4zx)
Ans.) We first multiply each term of (5x+3y – 4z) by 3xy, then multiply each term of (5x+3y – 4z ) by (- 7yz), and then we multiply each term of (5x+3y – 4z ) by 4zx. Finally, we add all the term –
Thus, (5x+3y – 4z ) X (3xy – 7yz + 4zx)
= (5x+3y – 4z ) X (3xy) + (5x+3y – 4z ) X (– 7yz) + (5x+3y – 4z ) X (4zx)
= (5X3).x.xy + (3X3).y.xy – (4X3).z.xy + (+)(-)(5X7).x.yz + (+)(-)(3X7).y.yz + (-)(-)(4X7).z.yz + (5X4).x.zx + (3X4).y.zx + (+)(-)(4X4).z.zx
= 15x¹⁺¹.y + 9x.y¹⁺¹ - 12xyz – 35xyz - 21.y¹⁺¹.z + 28y.z¹⁺¹ + 20x¹⁺¹.z + 12 xyz – 16.z¹⁺¹.x
= 15x²y + 9xy² - 35xyz – 21y²z + 28yz² + 20x²z – 16z²x (Ans.)