Intermediate Algebra Problems With Answers -
Sample 11 - Simplify Algebraic Expressions by Removing Brackets

This page features a collection of intermediate algebra problems focused on simplifying algebraic expressions. Students will practice using the distributive property to expand expressions and eliminate brackets. Fully worked solutions are provided at the bottom of the page for review and self-checking.

Problems

  1. Problems with one pair of brackets: Simplify by removing the brackets and grouping like terms.
    1. \( 2(3x + 4) + 6 \)
    2. \( -4(x + 3) - 7 \)
    3. \( -2(x - 2) + 4 \)
    4. \( -2(-x - 8) + 4 \)
    5. \( -\dfrac{3}{2}(-x - 8) + 4 \)
    6. \( -1.2(-2.2x - 1.7) + 0.2 \)
    7. \( 5(2x + 3y - 4) - x + 2y + 6 \)
    8. \( x(2x + 3y - 4) - x^2 + 4xy - 12 \)

  2. Problems with two pairs of brackets: Simplify by removing the brackets and grouping like terms.
    1. \( 3(x - 5) + 6(x + 3) \)
    2. \( -5(2x + 3) - 2(x - 3) \)
    3. \( (x - 2)(x + 3) + 8 \)
    4. \( (x - 2)^2 + 2(x - 4) \)
    5. \( y(x + 3) - x(2y + 4) - 7x - 8y + 2 \)

  3. Problems with nested brackets: Simplify by removing the brackets and grouping like terms.
    1. \( -2 \left( 3(x + 2) + 4 \right) - 8 \)
    2. \( 4 \left( -3x - 2(x - 9) \right) - 7(x - 2) \)
    3. \( 2 - \left( 3 - \left( -5(3x + 1) + 4 \right) \right) \)
    4. \( \left( (3 - x)(x + 2) + (-x + 4)(7x + 2) - (x - y)(2x - y) \right) - 3x^2 - 7x + 5 \)

Answers to the Above Problems

    1. \( 2(3x + 4) + 6 \)
      \( = 6x + 8 + 6 \)
      \( = 6x + 14 \)
    2. \( -4(x + 3) - 7 \)
      \( = -4x - 12 - 7 \)
      \( = -4x - 19 \)
    3. \( -2(x - 2) + 4 \)
      \( = -2x + 4 + 4 \)
      \( = -2x + 8 \)
    4. \( -2(-x - 8) + 4 \)
      \( = 2x + 16 + 4 \)
      \( = 2x + 20 \)
    5. \( -\dfrac{3}{2}(-x - 8) + 4 \)
      \( = \dfrac{3}{2}x + 12 + 4 \)
      \( = \dfrac{3}{2}x + 16 \)
    6. \( -1.2(-2.2x - 1.7) + 0.2 \)
      \( = 2.64x + 2.04 + 0.2 \)
      \( = 2.64x + 2.24 \)
    7. \( 5(2x + 3y - 4) - x + 2y + 6 \)
      \( = 10x + 15y - 20 - x + 2y + 6 \)
      \( = 9x + 17y - 14 \)
    8. \( x(2x + 3y - 4) - x^2 + 4xy - 12 \)
      \( = 2x^2 + 3xy - 4x - x^2 + 4xy - 12 \)
      \( = x^2 + 7xy - 4x - 12 \)

    1. \( 3(x - 5) + 6(x + 3) \)
      \( = 3x - 15 + 6x + 18 \)
      \( = 9x + 3 \)
    2. \( -5(2x + 3) - 2(x - 3) \)
      \( = -10x - 15 - 2x + 6 \)
      \( = -12x - 9 \)
    3. \( (x - 2)(x + 3) + 8 \)
      \( = x^2 + 3x - 2x - 6 + 8 \)
      \( = x^2 + x + 2 \)
    4. \( (x - 2)^2 + 2(x - 4) \)
      \( = x^2 - 4x + 4 + 2x - 8 \)
      \( = x^2 - 2x - 4 \)
    5. \( y(x + 3) - x(2y + 4) - 7x - 8y + 2 \)
      \( = yx + 3y - 2xy - 4x - 7x - 8y + 2 \)
      \( = -xy - 11x - 5y + 2 \)

    1. \( -2(3(x + 2) + 4) - 8 \)
      \( = -2(3x + 6 + 4) - 8 \)
      \( = -2(3x + 10) - 8 \)
      \( = -6x - 20 - 8 \)
      \( = -6x - 28 \)
    2. \( 4(-3x - 2(x - 9)) - 7(x - 2) \)
      \( = 4(-3x - 2x + 18) - 7x + 14 \)
      \( = 4(-5x + 18) - 7x + 14 \)
      \( = -20x + 72 - 7x + 14 \)
      \( = -27x + 86 \)
    3. \( 2 - \left( 3 - \left( -5(3x + 1) + 4 \right) \right) \)
      \( = 2 - \left( 3 - (-15x - 5 + 4) \right) \)
      \( = 2 - \left( 3 - (-15x - 1) \right) \)
      \( = 2 - (3 + 15x + 1) \)
      \( = 2 - (15x + 4) \)
      \( = 2 - 15x - 4 \)
      \( = -15x - 2 \)
    4. \( \left[ (3 - x)(x + 2) + (-x + 4)(7x + 2) - (x - y)(2x - y) \right] - 3x^2 - 7x + 5 \)
      \( = \left[ 3x + 6 - x^2 - 2x + (-7x^2 - 2x + 28x + 8) - (2x^2 - xy - 2yx + y^2) \right] - 3x^2 - 7x + 5 \)
      \( = \left[ -x^2 + x + 6 - 7x^2 + 26x + 8 - 2x^2 + xy + 2yx - y^2 \right] - 3x^2 - 7x + 5 \)
      \( = \left[ (-x^2 - 7x^2 - 2x^2) + (xy + 2yx) + (x + 26x) + 6 + 8 - y^2 \right] - 3x^2 - 7x + 5 \)
      \( = -10x^2 + 3xy + 27x - y^2 + 14 - 3x^2 - 7x + 5 \)
      \( = -13x^2 + 3xy - y^2 + 20x + 19 \)

More References and Links