Practice Maths

Expanding with the Distributive Law — Solutions

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  1. Expand using the distributive law

    1. 3(x+4):
    2. 5(2a+3):
    3. 4(m−7):
    4. 2(3b+8):
    5. 6(n+5):
    6. 7(2x−3):
    7. 9(p+1):
    8. 4(5k−2):

  2. Expand with negative outside

    1. −3(x+4):
    2. −2(5a−1):
    3. −4(m+6):
    4. −(n−8):
    5. −5(2b+3):
    6. −7(x−2):
    7. −3(4y+5):
    8. −6(3p−4):

  3. Expand then simplify

    1. 2(x+3)+4x:
    2. 3(2a+1)−5a:
    3. 4(m+2)+3(m+1):
    4. 5(b+4)−2(b−3):
    5. 3(n+5)+2(4n−1):
    6. 6(x−2)−3(2x+1):
    7. 4(3y+2)+5(2y−3):
    8. 2(5k−4)−3(k+6):

  4. Verify by substitution (x = 2)

    1. 4(x+3):
    2. 2(3x−5):
    3. −3(x+4):
    4. 5(2x−1)+3x:
    5. 2(x+6)−4(x−1):
    6. 3(2x+1)−2(3x−4):

  5. Find the missing value

    1. ?(x+3)=4x+12:
    2. 5(x+?)=5x+20:
    3. ?(x−2)=3x−6:
    4. ?(x+4)=−2x−8:
    5. 3(?+5)=3x+15:
    6. ?(2x+1)=6x+3:
    7. 4(3x−?)=12x−20:
    8. −?(x+6)=−5x−30:

  6. Problem solving

    1. Room area:
    2. Plumber cost:
    3. Garden area:
    4. Explanation:

  7. Expand with variable outside

    1. x(x+3):
    2. 2a(3a−4):
    3. m(5m+2):
    4. 3y(2y−7):
    5. 4b(b+6):
    6. −n(3n−5):
    7. 5k(2k+1):
    8. −2t(4t−3):

  8. Expand three-term brackets

    1. 2(x+3y−4):
    2. 5(a−2b+7):
    3. −3(m+4n−1):
    4. 4(2p+q−6):
    5. −(x−3y+2):
    6. 6(3a−b+5):

  9. Expand and simplify multi-bracket

    1. 3(x+2)+4(x−1)−2x:
    2. 2(3a−4)−(5a+2)+3a:
    3. 5(n+1)−3(n−2)+4(−n+3):
    4. −2(x+4)+3(2x−1)−4(x+5):
    5. 4(a+b)−3(a−2b)+a:
    6. 2x(x+3)−x(x−1)+4x:

  10. Multi-context problem solving

    1. Pencils:
    2. Pool perimeter:
    3. Camp cost:
    4. Student errors: