Answer:
The simplified given expression is
[tex]4x^3y^3.(3x^3-7xy^2+2xy-y)=12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4[/tex]
Step-by-step explanation:
Given expression is [tex]4x^3y^3.(3x^3-7xy^2+2xy-y)[/tex]
To simplify the given expression [tex]4x^3y^3.(3x^3-7xy^2+2xy-y)[/tex] :
By using Distributive property a.(bx+cd)=abx+acd
[tex]4x^3y^3.(3x^3-7xy^2+2xy-y)=(4x^3y^3).(3x^3)+(4x^3y^3).(-7xy^2)+(4x^3y^3).(2xy)+(4x^3y^3).(-y)[/tex] (by using distributive property )
[tex]=12x^3x^3y^3-28x^3xy^3y^2+8x^3xy^3y-4x^3y^3y[/tex] (by distributive property) and combining the like powers
[tex]=12x^{3+3}y^3-28x^{3+1}y^{3+2}+8x^{3+1}y^{3+1}-4x^3y^{3+1}[/tex] ( using [tex]a^m.a^n=a^{m+n}[/tex] ) summing the powers
[tex]=12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4[/tex] ( using [tex]a^m.a^n=a^{m+n}[/tex] )
Therefore [tex]4x^3y^3.(3x^3-7xy^2+2xy-y)=12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4[/tex]
Therefore the simplified expression is [tex]12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4[/tex]
