Multiplication of Polynomials
The multiplication operation on polynomials follows the general properties like commutative property, associative property, distributive property, etc. Applying these properties using the rules of exponents we can solve the multiplication of polynomials. To multiply to polynomials, we just multiply every term of one polynomial with every term of the other polynomial and then add all the results. Here is an example to multiply polynomials.
Example: (2x + 3y)(4x – 5y)
= 2x(4x – 5y) + 3y(4x – 5y)
= 8x2 – 10xy + 12xy – 15y2
⇒ 8x2 + 2xy – 15y2
Example: Solve (6x−3y)×(2x+5y)
Solution:
⇒ 6x ×(2x+5y)–3y × (2x+5y) ———- Using distributive law of multiplication
⇒ (12x2+30xy) – (6yx+15y2) ———- Using the distributive law of multiplication
⇒12x2+30xy–6xy–15y2 —————– as xy = yx
Thus, (6x−3y)×(2x+5y)=12x2+24xy−15y2