Question

Which expression represents the product of 2xy and 3xy+5y-xy^2

Answer 1

The product of
`2xy\: and\: 3xy+5y-xy^2` is
`\mathbf{6x^2y^2+10xy^2-2x^2y^3}`

Option D is correct answer.

Explanation:

We need to find Which expression represents the product of
`2xy\: and\: 3xy+5y-xy^2`

So, we need to multiply both expressions:

`(2xy) ( 3xy+5y-xy^2)`

We will multiply 2xy with each term inside the bracket

`=2xy(3xy)+2xy(5y)-2xy(xy^2)`

The same variables are multiplied and their powers are added i.e.
`a^m.a^n=a^(m+n)`

The constants are multiplied with the constants.

`=2(3)x^(1+1)y^(1+1)+2(5)xy^(1+1)-2x^(1+1)y^(1+2)\\=6x^2y^2+10xy^2-2x^2y^3`

So, the product of
`2xy\: and\: 3xy+5y-xy^2` is
`\mathbf{6x^2y^2+10xy^2-2x^2y^3}`

Option D is correct answer.