Question

An expression is shown below. Which expression is equivalent to the expression shown?

Answer 1

Note: In option A, it should be "+" instead of "(".

Given:

The expression is

$-2x(x+y-3)+3(-x+4y)+y(3x+5y-3)$

To find:

The equivalent expression.

Solution:

We have,

$-2x(x+y-3)+3(-x+4y)+y(3x+5y-3)$

Using distributive property, we get

$=-2x(x)-2x(y)-2x(-3)+3(-x)+3(4y)+y(3x)+y(5y)+y(-3)$

$=-2x^2-2xy+6x-3x+12y+3xy+5y^2-3y$

On combining like terms, we get

$=-2x^2+5y^2+(-2xy+3xy)+(6x-3x)+(12y-3y)$

$=-2x^2+5y^2+xy+3x+9y$

The expression $-2x^2+5y^2+xy+3x+9y$ is equivalent to the given expression.

Therefore, the correct option is A.