Eight Standard >> Algebraic Expressions | Multiplication of binomials and trinomials

Multiplication of a binomial or a trinomial by a binomial

Distributive law:
a.(b+c)=a(b)+a(c)

Example 1: \(5m^{2}n(2m+5n)\)
     =\(5m^{2}n \times 2m+5m^{2}n \times 5n\)
     =\(10m^{2+1}n+255m^{2}n^{1+1}\)
     =\(10m^{3}n+255m^{2}n^{2}\)

Example 2: \((3x^{2}y-5xy+2y^{2}) \times 3xy)\)

Solution: \(3x^{2}y \times 3xy -5xy \times 3xy +2y^{2} \times 3xy \)
       =\(9x^{2+1}y^{1+1} -15x^{1+1}y^{1+1} +6xy^{2+1}\)
       =\(9x^{3}y^{2} -15x^{2}y^{2} +6xy^{3}\) Ans.

Example 3: Find the product of \((x^{2}-2x)\) and \((x^{3}-3x+5)\) and verify the result when x=1

Solution: \((x^{2}-2x)\) \(\times\) \((x^{3}-3x+5)\)
       =\(x^{2}(x^{3}-3x+5)\) -\(2x(x^{3}-3x+5)\)
       =\(x^{2}x^{3}-x^{2}.3x+5x^{2}-2x.x^{3}+2x.3x-2x.5\)
       =\(x^{5}-3x^{3}+5x^{2}-2x^{4}+6x^{2}-10x\)
       =\(x^{5}-2x^{4}-3x^{3}+11x^{2}-10x\) Ans

\((x^{2}-2x)\) \(\times\) \((x^{3}-3x+5)\) 
Put x=1
=\((1^{2}-2.1)\) \(\times\) \((1^{3}-3.1+5)\) 
=(-1)3=-3

Put x=1 on the result
    \(1^{5}-2.1^{4}-3.1^{3}+11.1^{2}-10.1\)
   =1-2-3+11-10
   =12-15=-3

So both are same and verified.