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Zorluk: Çok zorSimplifying Algebraic Expressions

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

  • −3x[2y−(x−4y)]+2x(x−y)-3x[2y - (x - 4y)] + 2x(x - y)5x2−20xy5x^2 - 20xy
  • 4xy−2[x(3y−x)−y(x+2y)]4xy - 2[x(3y - x) - y(x + 2y)]2x2+4y22x^2 + 4y^2
  • x2(y−2)−[xy(x−3)−x(2x+y)]−xyx^2(y - 2) - [xy(x - 3) - x(2x + y)] - xy3xy3xy
  • −(2x−3y)(x+y)+x(2x+y)−y(x−3y)-(2x - 3y)(x + y) + x(2x + y) - y(x - 3y)xy+6y2xy + 6y^2

Cevap

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.

Adım Adım Çözüm

1
Simplify the first expression −3x[2y−(x−4y)]+2x(x−y)-3x[2y - (x - 4y)] + 2x(x - y).
The expression simplifies to 5x2−20xy5x^2 - 20xy.
By following the order of operations, innermost parentheses are cleared first, followed by distribution and combining like terms.
2
Simplify the second expression 4xy−2[x(3y−x)−y(x+2y)]4xy - 2[x(3y - x) - y(x + 2y)].
The expression simplifies to 2x2+4y22x^2 + 4y^2.
Expanding the terms inside the bracket yields −x2+2xy−2y2-x^2 + 2xy - 2y^2. Distributing the −2-2 flips the signs, and the xyxy terms successfully cancel.
3
Simplify the third expression x2(y−2)−[xy(x−3)−x(2x+y)]−xyx^2(y - 2) - [xy(x - 3) - x(2x + y)] - xy.
The expression simplifies to 3xy3xy.
Careful distribution of the negative sign across the simplified bracket (x2y−2x2−4xy)(x^2y - 2x^2 - 4xy) allows multiple high-degree terms to cancel out perfectly.
4
Simplify the fourth expression −(2x−3y)(x+y)+x(2x+y)−y(x−3y)-(2x - 3y)(x + y) + x(2x + y) - y(x - 3y).
The expression simplifies to xy+6y2xy + 6y^2.
FOILing the first binomial and keeping the negative sign outside ensures signs are correctly flipped before combining with the other distributed terms.

Anahtar Kavram

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

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