Lesson 1 of 5
Find a common factor, then recognize squares and cubes.
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Worked example · 1 of 8
Worked example
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Factor . Check: expands back to the difference of squares.
Big ideas
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The greatest common factor belongs to every term. Factor it out before applying another pattern, using the smallest shared power of each variable.
The difference of squares factors as . A sum does not use this pattern over the reals.
A perfect square has three terms: or . Check the middle term, not just the first and last.
The cube patterns are and . Expand to verify every sign.
Worked example
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Factor . Recognize and write . Expand to check that the quadratic and linear cross terms cancel.
Step-through
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Factor completely over integer coefficients.
Whole picture, 4 steps
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Worked example
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Worked example
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Mix-up alert
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Wrong idea: . Repair: the square expands to . A sum of squares is not a difference of squares.
Watch
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Flashcards
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Card 1 of 8
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Use the coefficient GCF and smaller exponent.
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What is the GCF of and ?
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Factor .
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Factor .
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Factor .
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Factor .
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Factor .
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How do you check a factorization?
Expand it and compare every original term.
Why take out a GCF first?
It simplifies the remaining expression and helps find all factors.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
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6 questions. One at a time.
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Write it
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Write it
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Start here if it helps: I can connect the conditions by...
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Match
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Connect the ideas
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