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

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

$3x(2x - 4) - 2(x^2 - 5x)$ $4x^2 - 2x$
$5(x^2 - 3x + 2) - 4x(x - 2)$ $x^2 - 7x + 10$
$-2x(3x + 1) + x(5x - 4)$ $-x^2 - 6x$
$4(2x^2 - x) - 3(x^2 + 2x - 1)$ $5x^2 - 10x + 3$

Answer

The correct pairings link each unsimplified expression with its resulting simplified polynomial after applying the distributive property and combining like terms.

Each unsimplified expression is accurately paired with its simplified equivalent by first applying the distributive property to eliminate all parentheses, rigorously managing negative multipliers, and finally grouping and combining all like terms according to their respective exponents.

Step-by-Step Solution

Expand and simplify the first expression.

6x^2 - 12x - 2x^2 + 10x

, which simplifies to

4x^2 - 2x

Applying the distributive property and combining the

x^2

terms and the

x

terms.

Expand and simplify the second expression.

5x^2 - 15x + 10 - 4x^2 + 8x

, which simplifies to

x^2 - 7x + 10

Distributing the constants and variables across parentheses, paying special attention to the negative signs.

Expand and simplify the third expression.

-6x^2 - 2x + 5x^2 - 4x

, which simplifies to

-x^2 - 6x

Multiplying each term inside the parentheses by the outside factor and combining the resulting like terms.

Expand and simplify the fourth expression.

8x^2 - 4x - 3x^2 - 6x + 3

, which simplifies to

5x^2 - 10x + 3

Distributing the

-3

correctly reverses the signs of all terms within the second polynomial.

Key Concept

Simplifying Algebraic Expressions

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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