Question

4x3y3·(3x3−7xy2+2xy−y)

Answer 1

The simplified given expression is

`4x^3y^3.(3x^3-7xy^2+2xy-y)=12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4`

Explanation:

Given expression is
`4x^3y^3.(3x^3-7xy^2+2xy-y)`

To simplify the given expression
`4x^3y^3.(3x^3-7xy^2+2xy-y)` :

By using Distributive property a.(bx+cd)=abx+acd

`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)` (by using distributive property )

`=12x^3x^3y^3-28x^3xy^3y^2+8x^3xy^3y-4x^3y^3y` (by distributive property) and combining the like powers

`=12x^(3+3)y^3-28x^(3+1)y^(3+2)+8x^(3+1)y^(3+1)-4x^3y^(3+1)` ( using
`a^m.a^n=a^(m+n)` ) summing the powers

`=12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4` ( using
`a^m.a^n=a^(m+n)` )

Therefore
`4x^3y^3.(3x^3-7xy^2+2xy-y)=12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4`

Therefore the simplified expression is
`12x^6y^3-28x^4y^5+8x^4y^4-4x^3y^4`