Match each unsimplified algebraic expression with its correctly simplified equivalent.

$2(3y + 4)$ $6y + 8$
$5y + 2y - 3$ $7y - 3$
$-3(y - 2)$ $-3y + 6$
$4y + 2z - y + 3z$ $3y + 5z$

Answer

The correct pairings map each unsimplified expression to its distributed and combined form.

Each expression on the left is matched with its simplified form on the right by accurately applying the distributive property and combining like terms.

Step-by-Step Solution

Simplify the first expression: 2(3y + 4).

6y + 8

Multiply the outer term 2 by both terms inside the parentheses (3y and 4).

Simplify the second expression: 5y + 2y - 3.

7y - 3

Add the coefficients of the like terms containing y (5 and 2).

Simplify the third expression: -3(y - 2).

-3y + 6

Distribute the -3, noting that a negative multiplied by a negative results in a positive (+6).

Simplify the fourth expression: 4y + 2z - y + 3z.

3y + 5z

Group and add the coefficients of the y terms together, and the z terms together.

Key Concept

Simplifying Algebraic Expressions

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