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.

$5x - 3(2x - 4)$ $-x + 12$
$3(2m - 5n) - 2(m - 3n)$ $4m - 9n$
$4x(x - 2) - x^2 + 5x$ $3x^2 - 3x$
$7y - 3[y - 2(y + 1)]$ $10y + 6$

Answer

The correctly simplified expressions are:

5x - 3(2x - 4)

matches with

-x + 12

;

3(2m - 5n) - 2(m - 3n)

matches with

4m - 9n

;

4x(x - 2) - x^2 + 5x

matches with

3x^2 - 3x

; and

7y - 3[y - 2(y + 1)]

matches with

10y + 6

Each unsimplified expression must be correctly expanded using the distributive property, ensuring that negative multipliers are applied to every term inside the parentheses. After expanding, grouping and adding the coefficients of like terms produces the single correct simplified equivalent provided in the match list.

Step-by-Step Solution

Distribute any coefficients or negative signs immediately outside of parentheses or brackets.

Terms are expanded (e.g.,

-3(2x - 4)

becomes

-6x + 12

Distribution removes grouping symbols, which is required before combining terms.

For expressions with nested grouping symbols, simplify from the innermost parentheses outward.

Complex expressions like

7y - 3[y - 2(y + 1)]

simplify step-by-step to

7y + 3y + 6

Following the order of operations ensures accurate distribution of multipliers.

Group and combine like terms (terms with the exact same variable and exponent).

The final canonical form is reached for each expression.

Combining like terms fully simplifies the polynomial into standard form.

Key Concept

Simplifying Algebraic Expressions

Estimated Time:1m 30s

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