GCSE Mathematics (9-1)
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    12.1 Expanding and factorising quadratics — Practise with help

    Warm-up: remember

    Answer these from memory. Do not look back at the section.

    1. Simplify 3x+5x3x+5x.
    2. Expand 2(x+3)2(x+3).
    Check the warm-up
    1. 8x8x.
    2. 2x+62x+6.

    If an answer differs, revisit Section 8.2 for collecting like terms and Section 8.3 for expanding a bracket.

    Practise with help

    1. Expand (x+2)(x+6)(x+2)(x+6).

    Hint

    Multiply each term in the first bracket by both terms in the second.

    Next step

    Use the hint to write the next algebra line. Then finish the calculation before opening the full working.

    Full working

    (x+2)(x+6)=x2+6x+2x+12=x2+8x+12(x+2)(x+6)=x^2+6x+2x+12=x^2+8x+12.

    2. Factorise x2+9x+20x^2+9x+20.

    Hint

    Find a pair with sum 99 and product 2020.

    Next step

    Use the hint to write the next algebra line. Then finish the calculation before opening the full working.

    Full working

    The pair is 4,54,5, so x2+9x+20=(x+4)(x+5)x^2+9x+20=(x+4)(x+5).

    Choose a method: factorise x2+7x+10x^2+7x+10. Which method applies, and why?

    Full working

    Factorisation applies because the expression is a monic quadratic with integer factors: x2+7x+10=(x+5)(x+2)x^2+7x+10=(x+5)(x+2).

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