Practice Maths

Factorising Algebraic Expressions — Solutions

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  1. Numeric HCF factorising

    1. 6x + 9:
    2. 10y − 15:
    3. 4a + 12:
    4. 8m − 20:
    5. 14p + 21:
    6. 6t − 18:
    7. 15n + 25:
    8. 12k − 30:

  2. Variable HCF factorising

    1. x² + 5x:
    2. 3y² − 7y:
    3. 4a² + 6a:
    4. 10m² − 15m:
    5. 8p² + 12p:
    6. 6t² − 9t:
    7. 5n² + 20n:
    8. 12k² − 8k:

  3. Full factorising (numeric and variable HCF)

    1. 6x² + 9x:
    2. 10y² − 15y:
    3. 4a² + 8a:
    4. 12m² − 18m:
    5. 15p² + 25p:
    6. 9b² − 6b:

  4. Three-term expressions

    1. 6x² + 9x + 3:
    2. 4y² − 8y + 12:
    3. 10a + 15a² − 5:
    4. 12m² + 6m − 18:
    5. 8t² + 4t + 16:
    6. 5(2k − 3) expanded and re-factorised:

  5. Negative factor

    1. −4x − 8:
    2. −6y + 9:
    3. −3a² − 12a:
    4. −10m² + 15m:

  6. Problem solving

    1. Rectangle:
    2. Garden:
    3. HCF of 6x² + 4x:
    4. Triangle side:

  7. Factorise with larger HCFs

    1. 18x + 27:
    2. 24y − 36:
    3. 15a + 35:
    4. 21m − 28:
    5. 16p + 40:
    6. 45n − 30:
    7. 12k + 48:
    8. 32b − 24:

  8. Three-term factorising

    1. 3x + 6y + 9:
    2. 4a − 8b + 12:
    3. 5m + 10n − 15:
    4. 6p² + 9p + 3:
    5. 10x² − 5x + 15:
    6. 8a² + 4a − 12:

  9. Expand to verify then re-factorise

    1. 3(4x + 5):
    2. 2y(3y − 7):
    3. 5(a2 + 2a − 3):
    4. 4m(2m + 5):
    5. 6p(p − 3):
    6. −2(3n + 8):

  10. HCF in context

    1. Field plots:
    2. Sandwiches:
    3. Rectangle dimensions:
    4. Equivalent expressions: