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Expressions & Simplifying: Classroom Packet

Grade 8 Algebra: Combining Like Terms

Name: ______________________Date: ____________Score: ____ / 6

Level 1

One variable

  1. 1. Simplify:
    3x+5x3x + 5x
  2. 2. Simplify:
    7a−2a7a - 2a
  3. 3. Simplify:
    4y+3+2y4y + 3 + 2y
  4. 4. Simplify:
    9m−m+49m - m + 4
  5. 5. Simplify:
    6+2k−1+3k6 + 2k - 1 + 3k
  6. 6. Simplify:
    −4n+10n−3-4n + 10n - 3

Answer Key

Level 1

  1. 1. 8x8x
  2. 2. 5a5a
  3. 3. 6y+36y + 3
  4. 4. 8m+48m + 4
  5. 5. 5k+55k + 5
  6. 6. 6n−36n - 3

Grade 8 Algebra: Combining Like Terms

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Two variables

  1. 1. Simplify:
    3x+2y+5x−y3x + 2y + 5x - y
  2. 2. Simplify:
    4a−3b−a+7b4a - 3b - a + 7b
  3. 3. Simplify:
    −2p+5q−6p−2q-2p + 5q - 6p - 2q
  4. 4. Simplify:
    x+y+x−y+4x + y + x - y + 4
  5. 5. Simplify:
    5m−2n+3−m+n5m - 2n + 3 - m + n
  6. 6. Simplify:
    −3c+8d−4+3c−d-3c + 8d - 4 + 3c - d

Answer Key

Level 2

  1. 1. 8x+y8x + y
  2. 2. 3a+4b3a + 4b
  3. 3. −8p+3q-8p + 3q
  4. 4. 2x+42x + 4
  5. 5. 4m−n+34m - n + 3
  6. 6. 7d−47d - 4

Grade 8 Algebra: Combining Like Terms

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Variables with exponents and fractions

  1. 1. Simplify:
    3x2+4x−x2+2x3x^2 + 4x - x^2 + 2x
  2. 2. Simplify:
    5a2−3a+2−2a2+a5a^2 - 3a + 2 - 2a^2 + a
  3. 3. Simplify:
    12x+34x\tfrac{1}{2}x + \tfrac{3}{4}x
  4. 4. Simplify:
    0.6y−1.5+0.4y+20.6y - 1.5 + 0.4y + 2
  5. 5. Simplify:
    2xy+3x−5xy+x2xy + 3x - 5xy + x
  6. 6. Simplify:
    4m2n−mn2+2m2n+3mn24m^2n - mn^2 + 2m^2n + 3mn^2

Answer Key

Level 3

  1. 1. 2x2+6x2x^2 + 6x
  2. 2. 3a2−2a+23a^2 - 2a + 2
  3. 3. 54x\tfrac{5}{4}x
  4. 4. y+0.5y + 0.5
  5. 5. −3xy+4x-3xy + 4x
  6. 6. 6m2n+2mn26m^2n + 2mn^2

Grade 8 Algebra: Distributive Property

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Expand a single bracket

  1. 1. Expand:
    2(x+3)2(x + 3)
  2. 2. Expand:
    5(y−4)5(y - 4)
  3. 3. Expand:
    3(2a+1)3(2a + 1)
  4. 4. Expand:
    4(3−m)4(3 - m)
  5. 5. Expand:
    x(x+2)x(x + 2)
  6. 6. Expand:
    6(2k−5)6(2k - 5)

Answer Key

Level 1

  1. 1. 2x+62x + 6
  2. 2. 5y−205y - 20
  3. 3. 6a+36a + 3
  4. 4. 12−4m12 - 4m
  5. 5. x2+2xx^2 + 2x
  6. 6. 12k−3012k - 30

Grade 8 Algebra: Distributive Property

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Negatives and combining

  1. 1. Expand:
    −3(x+4)-3(x + 4)
  2. 2. Expand:
    −(2y−7)-(2y - 7)
  3. 3. Simplify:
    2(x+5)+3x2(x + 5) + 3x
  4. 4. Simplify:
    4(a−2)−a4(a - 2) - a
  5. 5. Simplify:
    7−2(n+1)7 - 2(n + 1)
  6. 6. Expand:
    −4(−3p+2)-4(-3p + 2)

Answer Key

Level 2

  1. 1. −3x−12-3x - 12
  2. 2. −2y+7-2y + 7
  3. 3. 5x+105x + 10
  4. 4. 3a−83a - 8
  5. 5. −2n+5-2n + 5
  6. 6. 12p−812p - 8

Grade 8 Algebra: Distributive Property

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Multiple brackets

  1. 1. Simplify:
    3(x+2)+2(x−1)3(x + 2) + 2(x - 1)
  2. 2. Simplify:
    5(2a−1)−3(a+4)5(2a - 1) - 3(a + 4)
  3. 3. Simplify:
    x(x−3)+2(x+5)x(x - 3) + 2(x + 5)
  4. 4. Simplify:
    12(4y+6)−(y−1)\tfrac{1}{2}(4y + 6) - (y - 1)
  5. 5. Simplify:
    −2(3m−n)+4(m+2n)-2(3m - n) + 4(m + 2n)
  6. 6. Simplify:
    3[2(x+1)−x]3[2(x + 1) - x]

Answer Key

Level 3

  1. 1. 5x+45x + 4
  2. 2. 7a−177a - 17
  3. 3. x2−x+10x^2 - x + 10
  4. 4. y+4y + 4
  5. 5. −2m+10n-2m + 10n
  6. 6. 3x+63x + 6

Grade 8 Algebra: Evaluating Expressions

Name: ______________________Date: ____________Score: ____ / 6

Level 1

One variable, positive values

  1. 1. Evaluate for x = 4:
    3x+23x + 2
  2. 2. Evaluate for a = 5:
    10−a10 - a
  3. 3. Evaluate for y = 6:
    y2+1\dfrac{y}{2} + 1
  4. 4. Evaluate for n = 3:
    4n−74n - 7
  5. 5. Evaluate for m = 2:
    5(m+1)5(m + 1)
  6. 6. Evaluate for k = 10:
    2k−32k - 3

Answer Key

Level 1

  1. 1. 1414
  2. 2. 55
  3. 3. 44
  4. 4. 55
  5. 5. 1515
  6. 6. 1717

Grade 8 Algebra: Evaluating Expressions

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Negatives and exponents

  1. 1. Evaluate for x = -2:
    4x+94x + 9
  2. 2. Evaluate for a = 3:
    a2+1a^2 + 1
  3. 3. Evaluate for y = -3:
    y2−2yy^2 - 2y
  4. 4. Evaluate for n = -1:
    6−3n6 - 3n
  5. 5. Evaluate for m = 2:
    m3−4m^3 - 4
  6. 6. Evaluate for p = -4:
    p2−5\dfrac{p}{2} - 5

Answer Key

Level 2

  1. 1. 11
  2. 2. 1010
  3. 3. 1515
  4. 4. 99
  5. 5. 44
  6. 6. −7-7

Grade 8 Algebra: Evaluating Expressions

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Several variables

  1. 1. Evaluate for x = 2, y = 3:
    4x+2y4x + 2y
  2. 2. Evaluate for a = -1, b = 4:
    a2+3ba^2 + 3b
  3. 3. Evaluate for x = 3, y = -2:
    x2−xyx^2 - xy
  4. 4. Evaluate for m = 5, n = 2:
    m+nn\dfrac{m + n}{n}
  5. 5. Evaluate for r = 3 (use π ≈ 3.14):
    πr2\pi r^2
  6. 6. Evaluate for a = 2, b = -3, c = 1:
    b2−4acb^2 - 4ac

Answer Key

Level 3

  1. 1. 1414
  2. 2. 1313
  3. 3. 1515
  4. 4. 72\tfrac{7}{2}
  5. 5. 28.2628.26
  6. 6. 11

Grade 8 Algebra: Writing Algebraic Expressions from Words

Name: ______________________Date: ____________Score: ____ / 6

Level 1

One operation

  1. 1. Write as an expression:
    5\text{5}more\text{more}than\text{than}a\text{a}number\text{number}nn\text{}
  2. 2. Write as an expression:
    a\text{a}number\text{number}xx\text{}decreased\text{decreased}by\text{by}8\text{8}
  3. 3. Write as an expression:
    the\text{the}product\text{product}of\text{of}7\text{7}and\text{and}yy\text{}
  4. 4. Write as an expression:
    a\text{a}number\text{number}mm\text{}divided\text{divided}by\text{by}4\text{4}
  5. 5. Write as an expression:
    twice\text{twice}a\text{a}number\text{number}kk\text{}
  6. 6. Write as an expression:
    12\text{12}less\text{less}than\text{than}a\text{a}number\text{number}pp\text{}

Answer Key

Level 1

  1. 1. n+5n + 5
  2. 2. x−8x - 8
  3. 3. 7y7y
  4. 4. m4\dfrac{m}{4}
  5. 5. 2k2k
  6. 6. p−12p - 12

Grade 8 Algebra: Writing Algebraic Expressions from Words

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Two operations

  1. 1. Write as an expression:
    3\text{3}more\text{more}than\text{than}twice\text{twice}a\text{a}number\text{number}xx\text{}
  2. 2. Write as an expression:
    the\text{the}quotient\text{quotient}of\text{of}a\text{a}number\text{number}nn\text{}and\text{and}6,\text{6,}minus\text{minus}1\text{1}
  3. 3. Write as an expression:
    4\text{4}times\text{times}the\text{the}sum\text{sum}of\text{of}bb\text{}and\text{and}2\text{2}
  4. 4. Write as an expression:
    9\text{9}less\text{less}than\text{than}5\text{5}times\text{times}a\text{a}number\text{number}yy\text{}
  5. 5. Write as an expression:
    half\text{half}of\text{of}a\text{a}number\text{number}m,m\text{,}plus\text{plus}10\text{10}
  6. 6. Write as an expression:
    the\text{the}difference\text{difference}of\text{of}xx\text{}and\text{and}3,\text{3,}divided\text{divided}by\text{by}2\text{2}

Answer Key

Level 2

  1. 1. 2x+32x + 3
  2. 2. n6−1\dfrac{n}{6} - 1
  3. 3. 4(b+2)4(b + 2)
  4. 4. 5y−95y - 9
  5. 5. 12m+10\tfrac{1}{2}m + 10
  6. 6. x−32\dfrac{x - 3}{2}

Grade 8 Algebra: Writing Algebraic Expressions from Words

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Exponents and word problems

  1. 1. Write as an expression:
    the\text{the}square\text{square}of\text{of}a\text{a}number\text{number}n,n\text{,}increased\text{increased}by\text{by}7\text{7}
  2. 2. Write as an expression:
    the\text{the}sum\text{sum}of\text{of}a\text{a}number\text{number}and\text{and}its\text{its}square\text{square}
  3. 3. Write as an expression:
    Sam\text{Sam}has\text{has}dd\text{}dollars.\text{dollars.}Mia\text{Mia}has\text{has}6\text{6}dollars\text{dollars}less\text{less}than\text{than}3\text{3}times\text{times}Sam.\text{Sam.}How\text{How}much\text{much}does\text{does}Mia\text{Mia}have?\text{have?}
  4. 4. Write as an expression:
    A\text{A}phone\text{phone}plan\text{plan}costs\text{costs}20\text{20}dollars\text{dollars}plus\text{plus}0.10\text{0.10}dollars\text{dollars}per\text{per}text\text{text}tt\text{}
  5. 5. Write as an expression:
    the\text{the}perimeter\text{perimeter}of\text{of}a\text{a}rectangle\text{rectangle}with\text{with}length\text{length}ll\text{}and\text{and}width\text{width}4\text{4}
  6. 6. Write as an expression:
    the\text{the}product\text{product}of\text{of}3\text{3}and\text{and}a\text{a}number,\text{number,}decreased\text{decreased}by\text{by}the\text{the}square\text{square}of\text{of}the\text{the}number\text{number}

Answer Key

Level 3

  1. 1. n2+7n^2 + 7
  2. 2. x+x2x + x^2
  3. 3. 3d−63d - 6
  4. 4. 20+0.10t20 + 0.10t
  5. 5. 2l+82l + 8
  6. 6. 3x−x23x - x^2