Answer:
The product of [tex]2xy\: and\: 3xy+5y-xy^2[/tex] is [tex]\mathbf{6x^2y^2+10xy^2-2x^2y^3}[/tex]
Option D is correct answer.
Step-by-step explanation:
We need to find Which expression represents the product of [tex]2xy\: and\: 3xy+5y-xy^2[/tex]
So, we need to multiply both expressions:
[tex](2xy) ( 3xy+5y-xy^2)[/tex]
We will multiply 2xy with each term inside the bracket
[tex]=2xy(3xy)+2xy(5y)-2xy(xy^2)[/tex]
The same variables are multiplied and their powers are added i.e. [tex]a^m.a^n=a^{m+n}[/tex]
The constants are multiplied with the constants.
[tex]=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[/tex]
So, the product of [tex]2xy\: and\: 3xy+5y-xy^2[/tex] is [tex]\mathbf{6x^2y^2+10xy^2-2x^2y^3}[/tex]
Option D is correct answer.
