For all real numbers x and y, match each algebraic expression on the left with its simplif… — ACT

For all real numbers $x$ and $y$ , match each algebraic expression on the left with its simplified equivalent expression on the right.

The expression

2(x - 3y) + 4y

simplifies to

2x - 2y

, the expression

-2(x - 3y) + 8y

simplifies to

-2x + 14y

, and the expression

2(x + 3y) - 4y

simplifies to

2x + 2y

Each expression on the left-hand side is expanded by applying the distributive property and then simplified by combining the terms involving

y

. This correctly matches

2(x - 3y) + 4y

2x - 2y

-2(x - 3y) + 8y

-2x + 14y

, and

2(x + 3y) - 4y

2x + 2y

Simplify the expression

2(x - 3y) + 4y

2x - 2y

Distribute

2

to both terms inside the parentheses to get

2x - 6y

, then combine the like terms

-6y

and

4y

to get

-2y

Simplify the expression

-2(x - 3y) + 8y

-2x + 14y

Distribute

-2

to both terms inside the parentheses to get

-2x + 6y

, then combine the like terms

6y

and

8y

to get

14y

Simplify the expression

2(x + 3y) - 4y

2x + 2y

Distribute

2

to both terms inside the parentheses to get

2x + 6y

, then combine the like terms

6y

and

-4y

to get

2y

Simplifying algebraic expressions by distributing coefficients and combining like terms.

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