792 prompts matching "Structured question: binomial expansion with a negative term"
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Worked Example: Halving the coefficient of x and squaring it
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Practice: Working through a quadratic by completing the square, step by step
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Explain Back: An answer left in surd form after completing the square
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Common Mistakes: Checking a completed square by expanding it again
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Worked Example: Substituting a, b and c into the quadratic formula correctly
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Practice: Giving the roots correct to two decimal places
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Explain Back: Leaving the roots of a quadratic in surd form
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Show All Working: Choosing between factorising and the formula
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Common Mistakes: A sign error in the formula, and how to catch it
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Worked Example: The product of the roots as c over a
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Practice: Forming an equation from a given sum and product
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Explain Back: Finding a missing coefficient from a stated sum of roots
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Show All Working: Roots equal in magnitude but opposite in sign
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Common Mistakes: Roots that are reciprocals of one another
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Worked Example: The identity linking alpha squared plus beta squared to the sum and product
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Practice: The value of alpha to the fourth plus beta to the fourth
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Explain Back: The value of alpha minus beta, all squared
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Show All Working: Forming an equation whose roots are three alpha and three beta
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Common Mistakes: A symmetric function needing the sum and product twice over
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Worked Example: Substituting into the quadratic and tidying up
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