755 prompts matching "Factorising fully, and knowing when to stop"
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Practice: An operation that is not commutative, with a counter-example
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Common Mistakes: Subtraction as an example of neither law
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Practice: Multiplication distributing over addition in ordinary arithmetic
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Common Mistakes: Distributivity on a set of three elements
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Final Revision: Why distributivity links two operations rather than one
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Learn: What an identity element is
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Practice: Why an identity element must work from both sides
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Common Mistakes: Checking an inverse by working the operation both ways
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Final Revision: Evaluating a numerical expression using the index laws
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Common Mistakes: Writing a root as a fractional index before simplifying
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Final Revision: Converting an answer back out of index form
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Common Mistakes: An indicial equation solved by substitution
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Final Revision: Checking an indicial solution by substitution
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Learn: The definition of a logarithm as the index
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Common Mistakes: Reading a logarithm from a table
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Learn: The law for the logarithm of a product
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Common Mistakes: Rejecting a root that makes a logarithm undefined
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Final Revision: Proving a logarithmic identity from the laws
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Learn: The change of base formula
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Common Mistakes: A logarithmic equation that becomes a quadratic
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