Answered

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An expression is shown below. Which expression is equivalent to the expression shown?
- 2x(x + y - 3) + 3(-x + 4y) + y(3x + 5y - 3)
- 2x2(5y2 + xy + 3x + 9y
- 2x2 + 5y2 + xy - 6x +9y
- 5x2 + 5y2 + xy + 3x + 9y
- 5x2 + 5y2 + xy - 6x + 9y

Sagot :

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.

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