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

A set of intermediate algebra problems, related to simplifying algebraic expressions by using the distributivity property to remove brackets is presented. The solutions to these problems are at the bottom of the page.


  1. Problems with one pair of brackets: Simplify by removing the brackets and grouping like terms.
    a) 2 ( 3x + 4 ) + 6
    b) -4 ( x + 3 ) - 7
    c) -2 ( x - 2 ) + 4
    d) -2 ( -x - 8 ) + 4
    e) -(3/2) ( -x - 8 ) + 4
    f) -1.2 ( -2.2x - 1.7 ) + 0.2
    g) 5(2x + 3y -4) - x + 2y + 6
    h) x(2x + 3y -4) - x 2 + 4xy - 12

  2. Problems with two pairs of brackets: Simplify by removing the brackets and grouping like terms.
    a) 3 ( x - 5 ) + 6 ( x + 3 )
    b) -5 ( 2x + 3 ) - 2 ( x - 3 )
    c) ( x - 2 ) ( x + 3 ) + 8
    d) (x - 2) 2 + 2 ( x - 4 )
    e) y(x + 3) - x(2y + 4) - 7x - 8y + 2

  3. Problems with nested brackets: Simplify by removing the brackets and grouping like terms.
    a) -2 ( 3 ( x + 2 ) + 4 ) - 8
    b) 4 ( -3x - 2 ( x - 9) ) - 7 ( x - 2)
    c) 2 - ( 3 - ( -5 ( 3x + 1 ) + 4 ) )
    d) [ (3 - x) (x + 2) + (-x + 4) (7x + 2) - (x - y) (2x - y) ] - 3x 2 - 7x + 5

Answers to the Above Questions
  1. a) 2 ( 3x + 4 ) + 6
    = 6x + 8 + 6
    = 6x + 14
    b) -4 ( x + 3 ) - 7
    = -4x - 12 - 7
    = -4x - 19
    c) -2 ( x - 2 ) + 4
    = -2x + 4 + 4
    = -2x + 8
    d) -2 ( -x - 8 ) + 4
    = 2x + 16 + 4
    = 2x + 20
    e) -(3/2) ( -x - 8 ) + 4
    = (3/2)x + 12 + 4
    = (3/2)x + 16
    f) -1.2 ( -2.2x - 1.7 ) + 0.2
    = 2.64x + 2.04 + 0.2
    = 2.64x + 2.24
    g) 5(2x + 3y - 4) - x + 2y +6
    = 10x + 15y - 20 - x + 2y + 6
    = 9x + 17y - 14
    h) x(2x + 3y -4) - x 2 + 4xy - 12
    = 2x 2 + 3xy - 4x - x 2 + 4xy - 12
    = x 2 + 7xy - 4x - 12

  2. a) 3 ( x - 5 ) + 6 ( x + 3 )
    = 3x - 15 + 6x + 18
    = 9x + 3
    b) -5 ( 2x + 3 ) - 2 ( x - 3 )
    = -10x - 15 -2x + 6
    = -12x - 9
    c) ( x - 2 ) ( x + 3 ) + 8
    = x 2 + 3x - 2x - 6 + 8
    = x 2 + x + 2
    d) (x - 2) 2 + 2 ( x - 4 )
    = x 2 -4x + 4 + 2x - 8
    = x 2 -2x - 4
    e) y(x + 3) - x(2y + 4) - 7x - 8y + 2
    = yx + 3y - 2xy - 4x - 7x - 8y + 2
    = -xy - 11x - 5y + 2

  3. a) -2 ( 3 ( x + 2 ) + 4 ) - 8
    = -2 ( 3x + 6 + 4) - 8
    = -2 ( 3x + 10 ) - 8
    = -6x - 20 - 8
    = -6x - 28
    b) 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
    c) 2 - ( 3 - ( -5 ( 3x + 1 ) + 4 ) )
    = 2 - ( 3 - ( -15x - 5 + 4))
    = 2 - (3 - (-15x - 1))
    = 2 - (3 + 15x + 1)
    = 2 - (15x + 4)
    = 2 - 15x - 4
    = -15x - 2
    d) [ (3 - x) (x + 2) + (-x + 4) (7x + 2) - (x - y) (2x - y) ] - 3x 2 - 7x + 5
    = [ (3x + 6 - x 2 - 2x) + (- 7x 2 - 2x + 28x + 8) - (2x 2 - xy - 2yx + y 2) ] - 3x 2 - 7x + 5
    = [ - x 2 + x + 6 - 7x 2 + 26x + 8 - 2x 2 + xy + 2yx - y 2 ] - 3x 2 - 7x + 5
    = [ (- x 2 - 7x 2 - 2x 2 ) + (xy + 2yx )+ (x + 26x) + 6 + 8 - y 2 ] - 3x 2 - 7x + 5
    = -10x 2 + 3xy + 27x - y 2 + 14 - 3x 2 - 7x + 5
    = -13x 2 + 3xy - y 2 + 20x + 19

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