[discia] GCSE Maths › Algebra › Expanding and Factorising Quadratics

Expanding and Factorising Quadratics

discia.org 10 questions · 22 marks
Name Date
  1. Non-calculator 1 mark
    Which one of these expressions is equivalent to \(x^2 + 7x + 12\)?
    A \((x + 12)(x + 1)\) B \((x + 3)(x + 4)\) C \((x - 3)(x - 4)\) D \((x + 2)(x + 5)\)
    Write down the letter of your answer.
    Show answer
    Option B
    Another like this
  2. Non-calculator 2 marks

    Expand and simplify \((3x - 2)(4x - 5)\)

    Show answer
    \(12x^2 - 23x + 10\)
    Another like this
  3. Non-calculator 2 marks

    Multiply out the brackets and simplify \((3t - 4)^2\)

    Show answer
    \(9t^2 - 24t + 16\)
    Another like this
  4. Non-calculator 2 marks

    Factorise \(w^2 - 4w - 32\)

    Show answer
    \((w + 4)(w - 8)\)
    Another like this
  5. Non-calculator 2 marks

    \((t - 6)(t + a) = t^2 - 9t + 18\)

    Calculate the value of \(a\).

    Show answer
    \(-3\)
    Another like this
  6. Non-calculator 4 marks

    Show, by expanding and simplifying, that \((4x - 7)(x - 6) + 3x(x + 1) - 7(x^2 - 4x + 4)\) is equal to an integer.

    Show answer
    The \(x^2\) terms and the \(x\) terms both cancel, leaving the integer \(14\).
    Another like this
  7. Non-calculator 3 marks

    \((x + a)(x - 4a) \equiv x^2 + bx - 16\)

    Find the two possible values of \(b\).

    Show answer
    \(b = -6\) or \(b = 6\)
    Another like this
  8. Non-calculator 3 marks

    \(s\) and \(t\) are positive integers.

    \((m - s)(m + t)\) expands and simplifies to \(m^2 - km - 80\), where \(k\) is a positive integer.

    Work out the smallest possible value of \(k\).

    Show answer
    \(2\)
    Another like this
  9. Non-calculator 1 mark
    Factorise \(x^2 - 121\).
    A \((x - 11)^2\) B \(x(x - 121)\) C \((x + 11)^2\) D \((x + 11)(x - 11)\)
    Write down the letter of your answer.
    Show answer
    Option D
    Another like this
  10. Non-calculator 2 marks

    Expand and simplify \((5x + 1)(4x + 7)\)

    Show answer
    \(20x^2 + 39x + 7\)
    Another like this
discia.org Expanding and Factorising Quadratics · sheet 1
Answers Expanding and Factorising Quadratics · sheet 1
  1. Option B
  2. \(12x^2 - 23x + 10\)
  3. \(9t^2 - 24t + 16\)
  4. \((w + 4)(w - 8)\)
  5. \(-3\)
  6. The \(x^2\) terms and the \(x\) terms both cancel, leaving the integer \(14\).
  7. \(b = -6\) or \(b = 6\)
  8. \(2\)
  9. Option D
  10. \(20x^2 + 39x + 7\)
discia.org Expanding and Factorising Quadratics · sheet 1