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Perfect squares, difference of squaresFact

Fact

Perfect squares, difference of squares

Expand squares in full and factor differences fast

2 min 2 steps

Three identities cover most of the squaring and factoring on the test. I memorized the janitor's rounds faster than this, and for worse reasons.

Square and difference identitiesLearn it
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The first step is free. A free account opens the rest.

Used by

Distribute and expandTechniqueMultiply every term by every term, signs included
Factor polynomialsTechniquePull out the common factor, then match a pattern
Complete the squareTechniqueAdd half the x-coefficient, squared, to both sides
Square both sides and checkTechniqueIsolate the radical, square, then test every solution