Match each unsimplified algebraic expression on the left with its completely simplified eq… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each unsimplified algebraic expression on the left with its completely simplified equivalent on the right.

$3(2a - b) - 4(a + 2b)$ $2a - 11b$
$-2(a - 3b) + 5(2a - b)$ $8a + b$
$a(3 - 2b) - 2(a - ab)$ $a$
$4a - [2b - 3(a - b)]$ $7a - 5b$

Answer

The unsimplified expressions must be correctly expanded using the distributive property, observing proper handling of negative multipliers and nested grouping symbols, and then reduced by combining like terms.

Each expression correctly matches its fully reduced polynomial form. The reductions require systematic application of the distributive property, careful tracking of positive and negative coefficients, and the grouping and addition of like variables.

Step-by-Step Solution

Simplify the first expression:

3(2a - b) - 4(a + 2b)

6a - 3b - 4a - 8b = 2a - 11b

Multiply each term inside the parentheses by the outside factor, then group like terms (

6a - 4a

and

-3b - 8b

Simplify the second expression:

-2(a - 3b) + 5(2a - b)

-2a + 6b + 10a - 5b = 8a + b

Properly distribute the negative sign in the first term (

-2 \times -3b = 6b

), then combine like terms.

Simplify the third expression:

a(3 - 2b) - 2(a - ab)

3a - 2ab - 2a + 2ab = a

Distribute the variables and constants, recognizing that

-2ab

and

+2ab

are additive inverses and cancel to zero.

Simplify the fourth expression:

4a - [2b - 3(a - b)]

4a - [2b - 3a + 3b] = 4a - [5b - 3a] = 4a - 5b + 3a = 7a - 5b

Work from the innermost parentheses outward. Distribute

-3

, combine like terms inside the bracket, and distribute the outer negative sign.

Key Concept

Simplifying Algebraic Expressions

Estimated Time:2m 0s

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