Expanding and Factorising Quadratics worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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2 marks
Expand and simplify \((2y - 7)(3y - 7)\)
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2 marks
Expand and simplify \((2x + 7)^2\)
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2 marks
Write \(w^2 + 6w + 5\) as a product of two brackets.
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3 marks
(a)
Expand and simplify \((w + 11)(w - 11)\)
(b)Factorise \(16w^2 - 49\)
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2 marks
\((y + 5)(y + a) = y^2 + 10y + 25\)
Calculate the value of \(a\).
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2 marks
Factorise fully \(2y^2 - 11y - 6\)
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2 marks
Write \((4t + 5)(2t - 3)\) in the form \(at^2 + bt + c\), where \(a\), \(b\) and \(c\) are integers.
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2 marks
Write \((w + 4)^2\) in the form \(aw^2 + bw + c\), where \(a\), \(b\) and \(c\) are integers.
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2 marks
Factorise \(t^2 - 9t + 18\)
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3 marks
(a)
Multiply out the brackets and simplify \((k + 9)(k - 9)\)
(b)Factorise completely \(25k^2 - 4\)
Answers
- \(6y^2 - 35y + 49\)
- \(4x^2 + 28x + 49\)
- \((w + 5)(w + 1)\)
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(a) \(w^2 - 121\)
(b) \((4w + 7)(4w - 7)\) - \(5\)
- \((2y + 1)(y - 6)\)
- \(8t^2 - 2t - 15\)
- \(w^2 + 8w + 16\)
- \((t - 6)(t - 3)\)
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(a) \(k^2 - 81\)
(b) \((5k + 2)(5k - 2)\)