Match each unsimplified algebraic expression with its correctly simplified polynomial equi… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each unsimplified algebraic expression with its correctly simplified polynomial equivalent.

$3x - 2(x - 5) + 4$ $x + 14$
$5(2x^2 - x) - 3x(x + 2)$ $7x^2 - 11x$
$4x - [2x + 3(x - 1)]$ $-x + 3$
$\frac{1}{2}(4x - 6) + 3(x + 2)$ $5x + 3$

Answer

The correct matches pair each unsimplified expression with its corresponding standard form by applying the distributive property and carefully combining like terms.

Each correct pairing is derived by rigorously applying the distributive property, adhering to the order of operations for nested groupings, and grouping matching polynomial degrees correctly.

Step-by-Step Solution

Simplify the first expression:

3x - 2(x - 5) + 4

x + 14

Apply the distributive property to

-2(x - 5)

to get

-2x + 10

. Then combine like terms:

(3x - 2x) + (10 + 4)

Simplify the second expression:

5(2x^2 - x) - 3x(x + 2)

7x^2 - 11x

Distribute

5

to get

10x^2 - 5x

, and distribute

-3x

to get

-3x^2 - 6x

. Group like terms:

(10x^2 - 3x^2) + (-5x - 6x)

Simplify the third expression:

4x - [2x + 3(x - 1)]

-x + 3

Follow the order of operations by simplifying the innermost grouping first:

3(x - 1) = 3x - 3

. The brackets become

[5x - 3]

. Distributing the subtraction gives

4x - 5x + 3

Simplify the fourth expression:

\frac{1}{2}(4x - 6) + 3(x + 2)

5x + 3

Multiply coefficients:

\frac{1}{2}(4x) - \frac{1}{2}(6) = 2x - 3

, and

3(x) + 3(2) = 3x + 6

. Combine

x

terms and constants:

(2x + 3x) + (-3 + 6)

Key Concept

Simplifying Algebraic Expressions

Question

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