Equivalent expressions and the distributive property Knowledge-Based Practice

Questions

1. 1.

   Which expression is equivalent to $2x(3x - 4) - 5(x^2 - 2x + 1)$?

   • A) $x^2 - 18x - 5$
   • B) $x^2 - 2x - 5$
   • C) $x^2 + 2x - 5$
   • D) $x^2 + 2x + 5$
2. 2.

   Which expression is equivalent to $3x(4x - 5) - 2x(x - 6)$?

   • A) $10x^2 - 27x$
   • B) $10x^2 - 3x$
   • C) $14x^2 - 27x$
   • D) $10x^2 + 3x$
3. 3.

   Which expression is equivalent to $2[3(x - 4) - 5(2 - x)]$?

   • A) $-4x - 44$
   • B) $8x - 28$
   • C) $16x - 22$
   • D) $16x - 44$
4. 4.

   Which expression is equivalent to $(2x - 3)(x + 4)$?

   • A) $2x^2 - 12$
   • B) $2x^2 + 11x - 12$
   • C) $2x^2 - 5x - 12$
   • D) $2x^2 + 5x - 12$
5. 5.

   Which expression is equivalent to $x(3x + 4) - 3(x^2 - 2)$?

   • A) $6x^2 + 4x - 6$
   • B) $6x^2 + 4x + 6$
   • C) $4x - 6$
   • D) $4x + 6$
6. 6.

   When the expression $4(2x - 3) - 3(x - 5)$ is written in the equivalent form $ax + b$, what is the value of $a + b$?

   • A) 8
   • B) -22
   • C) -3
   • D) 2
7. 7.

   Which pair of expressions is equivalent for all values of $x$?

   • A) $3(2x + 5) - 4$ and $6x + 1$
   • B) $4(3x - 2) + 5$ and $12x + 3$
   • C) $5(x + 4) - 2x$ and $3x + 4$
   • D) $2(6x - 3) + 7$ and $12x + 1$
8. 8.

   Which expression is equivalent to $\frac{24x - 36}{6} - (3x - 5)$?

   • A) $x - 1$
   • B) $x - 11$
   • C) $7x - 1$
   • D) $x + 1$
9. 9.

   For what value of $a$ is the expression $a(3x - 4) + 2(x + 5)$ equivalent to $14x - 6$?

   • A) 2
   • B) 3
   • C) 4
   • D) 6
10. 10.

    Which expression is equivalent to $0.5(6x - 8) - 0.25(4x - 12)$?

    • A) $2x - 7$
    • B) $4x - 7$
    • C) $2x + 1$
    • D) $2x - 1$
11. 11.

    Which expression is equivalent to $-2(3x - 4y + 7) + 5(2x - y)$?

    • A) $4x - 13y - 14$
    • B) $4x + 3y + 14$
    • C) $16x + 3y - 14$
    • D) $4x + 3y - 14$
12. 12.

    Which expression is equivalent to $\frac{3}{5}(15x - 20) + 7x$?

    • A) $16x - 12$
    • B) $16x - 20$
    • C) $2x - 12$
    • D) $16x + 12$
13. 13.

    Which expression is equivalent to $8 - 3(4x - 5)$?

    • A) $20x - 25$
    • B) $-12x - 7$
    • C) $-12x + 13$
    • D) $-12x + 23$
14. 14.

    Which expression is equivalent to $48x - 32y + 16$?

    • A) $16(3x - 2y)$
    • B) $16(3x - 2y + 16)$
    • C) $16(3x - 2y - 1)$
    • D) $16(3x - 2y + 1)$
15. 15.

    Which expression is equivalent to $5(2x - 3) - 3(x - 4)$?

    • A) $7x - 27$
    • B) $7x + 3$
    • C) $10x - 3$
    • D) $7x - 3$

Answers and step-by-step solutions appear after you finish the test.