Eight Standard >> Operations on algebraic expressions | Multiplication and division operation

Multiplication of Binomial or trinomial by a monomial

1) When multiply two monomials tho things need to remember

 i) If both are plus then the product should be plus.
      (+)(+)=(+)
ii) If one is plus and another is minus then the product should be minus.
     (+)(-)=(-)
     (-)(+)=(-)
 i) If both are minus then product should be plus.

2) Law of exponence will be apply
   \(a^{m} \times a^{n}=a^{m+n}\)

Example 1:
    \(3x^{2}y^{3} \times -2xy^{4}\)
  =\((3 \times -2).x^{2+1}.y^{3+4}\)
  =\(-6x^{3}y^{7}\)
  
Example 2:
 \(15a^{3}xy^{2} \times -\frac{1}{5}ax^{2}y^{3} \times \frac{1}{3}a^{2}y^{3}\)
  =\((15 \times -\frac{1}{5} \times \frac{1}{3})a^{3+1+2}.x^{1+2}.y^{2+3+3}\)
  =\(-1a^{6}x^{3}y^{8}\)