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Flashcards · Maths · Algebra

Factorising Expressions

17 cards

  1. What is the first step in any factorising question?

    Take out the highest common factor.

  2. Factorise \(6x + 15\).

    \(3(2x + 5)\).

  3. Factorise fully \(6x^2y - 9xy^2\).

    \(3xy(2x - 3y)\).

  4. How do you know an expression is fully factorised?

    Nothing is left that divides into every term inside the brackets.

  5. What two numbers do you need to factorise \(x^2 + bx + c\)?

    Two numbers that multiply to give \(c\) and add to give \(b\).

  6. Factorise \(x^2 + 7x + 12\).

    \((x + 3)(x + 4)\).

  7. Factorise \(x^2 - 2x - 15\).

    \((x - 5)(x + 3)\).

  8. How can you check a factorisation?

    Expand the brackets and see whether you get the original expression back.

  9. What is the difference of two squares rule?

    \(a^2 - b^2 = (a + b)(a - b)\).

  10. Factorise \(x^2 - 49\).

    \((x + 7)(x - 7)\).

  11. Factorise \(4x^2 - 25\).

    \((2x + 5)(2x - 5)\).

  12. Why does \(x^2 + 49\) not factorise?

    It is a sum of squares. No pair of numbers multiplies to 49 and adds to 0.

  13. How can you work out \(51^2 - 49^2\) without a calculator?

    \((51 + 49)(51 - 49) = 100 \times 2 = 200\).

  14. What is the factorised form of \(x^2 + 6x + 9\)?

    \((x + 3)^2\), a perfect square.

  15. How do you factorise \(2x^2 + 7x + 3\) (Higher tier)?

    Multiply \(2 \times 3 = 6\), split the middle term as \(6x + x\), and factorise in pairs: \((2x + 1)(x + 3)\).

  16. How do you simplify \(\dfrac{x^2 - 9}{x + 3}\) (Higher tier)?

    Factorise the top to \((x + 3)(x - 3)\), cancel the common bracket and get \(x - 3\).

  17. Why can you not cancel the \(x\) in \(\dfrac{x + 6}{x}\)?

    The \(x\) is only one term of the top, not a factor of the whole top, so the expression does not simplify to 6.