AQA · Mathematics · 8300
GCSE Maths: Algebra: expanding two brackets
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Algebra: expanding two brackets (Corbettmaths Video 14), 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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What is the first step when expanding two brackets such as (x + 3)(x + 5)?
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Multiply each term in the first bracket by each term in the second bracket (often remembered as FOIL: First, Outer, Inner, Last).
Expand and simplify (x + 4)(x + 2)
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x² + 6x + 8
Expand and simplify (x + 5)(x − 3)
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x² + 2x − 15
Expand and simplify (x − 4)(x − 3)
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x² − 7x + 12
What special pattern emerges when expanding (a + b)(a − b)?
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The result is a² − b² (difference of two squares). The middle terms cancel out.
Expand and simplify (x + 7)(x − 7)
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x² − 49
Expand and simplify (2x + 3)(x + 4)
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2x² + 11x + 12
Expand and simplify (3x − 2)(2x + 5)
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6x² + 11x − 10
What is the general result when expanding (a + b)²?
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a² + 2ab + b². The middle term is twice the product of the two terms.
Expand and simplify (x + 5)²
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x² + 10x + 25
Expand and simplify (x − 4)²
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x² − 8x + 16
Expand and simplify (2x + 3)²
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4x² + 12x + 9
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