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

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

$-3x[2y - (x - 4y)] + 2x(x - y)$ $5x^2 - 20xy$
$4xy - 2[x(3y - x) - y(x + 2y)]$ $2x^2 + 4y^2$
$x^2(y - 2) - [xy(x - 3) - x(2x + y)] - xy$ $3xy$
$-(2x - 3y)(x + y) + x(2x + y) - y(x - 3y)$ $xy + 6y^2$

Answer

The correct pairings match each multi-step expression to its exact simplified polynomial counterpart: L1 matches R1, L2 matches R2, L3 matches R3, and L4 matches R4.

Each correct match is formed by strictly following the order of operations: clearing innermost groupings first, distributing outer multipliers across all contained terms, and combining structurally identical variable terms into standard canonical form.

Step-by-Step Solution

Simplify the first expression

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

The expression simplifies to

5x^2 - 20xy

By following the order of operations, innermost parentheses are cleared first, followed by distribution and combining like terms.

Simplify the second expression

4xy - 2[x(3y - x) - y(x + 2y)]

The expression simplifies to

2x^2 + 4y^2

Expanding the terms inside the bracket yields

-x^2 + 2xy - 2y^2

. Distributing the

-2

flips the signs, and the

xy

terms successfully cancel.

Simplify the third expression

x^2(y - 2) - [xy(x - 3) - x(2x + y)] - xy

The expression simplifies to

3xy

Careful distribution of the negative sign across the simplified bracket

(x^2y - 2x^2 - 4xy)

allows multiple high-degree terms to cancel out perfectly.

Simplify the fourth expression

-(2x - 3y)(x + y) + x(2x + y) - y(x - 3y)

The expression simplifies to

xy + 6y^2

FOILing the first binomial and keeping the negative sign outside ensures signs are correctly flipped before combining with the other distributed terms.

Key Concept

Simplifying complex algebraic expressions through precise application of the distributive property, order of operations (PEMDAS), and combination of like terms.

Estimated Time:4m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic