Note: In option A, it should be "+" instead of "(".
Given:
The expression is
[tex]-2x(x+y-3)+3(-x+4y)+y(3x+5y-3)[/tex]
To find:
The equivalent expression.
Solution:
We have,
[tex]-2x(x+y-3)+3(-x+4y)+y(3x+5y-3)[/tex]
Using distributive property, we get
[tex]=-2x(x)-2x(y)-2x(-3)+3(-x)+3(4y)+y(3x)+y(5y)+y(-3)[/tex]
[tex]=-2x^2-2xy+6x-3x+12y+3xy+5y^2-3y[/tex]
On combining like terms, we get
[tex]=-2x^2+5y^2+(-2xy+3xy)+(6x-3x)+(12y-3y)[/tex]
[tex]=-2x^2+5y^2+xy+3x+9y[/tex]
The expression [tex]-2x^2+5y^2+xy+3x+9y[/tex] is equivalent to the given expression.
Therefore, the correct option is A.
