AQA · Mathematics · 8300
GCSE Maths: Factorisation: difference of 2 squares
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Factorisation: difference of 2 squares (Corbettmaths Video 120), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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The factorisation x² − 121 uses the ? formula.
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difference of two squares
What is the general formula for the difference of two squares?
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a² − b² = (a + b)(a − b)
Factorise x² − 121
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(x + 11)(x − 11)
Factorise y² − 9w²
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(y + 3w)(y − 3w)
When factorising x² − 11x + 30, what is the error in the answer (x + 5)(x + 6)?
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The signs should be negative: (x − 5)(x − 6), because the middle term is −11x and the constant is positive.
What is the first step when factorising 2y² − 50 fully?
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Factor out the common factor 2 to get 2(y² − 25), then factorise y² − 25 as a difference of two squares.
Factorise 2y² − 50 fully
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2(y + 5)(y − 5)
For the quadratic x² + ax + 24 where a is a positive integer, how many possible values exist for a?
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4 possible values (corresponding to factor pairs of 24: 1+24=25, 2+12=14, 3+8=11, 4+6=10)
Factorise (x + 4)² + 3(x + 4) fully
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(x + 4)(x + 7)
If 10x² + 9x + 2 = (5x + 2)(2x + 1), what is the factorisation of 10(y − 3)² + 9(y − 3) + 2?
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(5(y − 3) + 2)(2(y − 3) + 1) or equivalently (5y − 13)(2y − 5)
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