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FACTORING SPECIAL FACTORING SPECIAL PRODUCTSPRODUCTS
FORMULAS TO FORMULAS TO MEMORIZE!MEMORIZE!
Section 6.3
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FORMULAS… Memorize FORMULAS… Memorize these! these! Perfect Square Trinomials:
◦a2 + 2ab + b2 = (a + b)2
Difference of 2 Squares:◦a2 - b2 = (a + b)(a – b)
Difference of 2 Cubes:◦a3 – b3 = (a – b)(a2 + ab + b2)
Sum of 2 Cubes:◦a3 + b3 = (a +b)(a2 - ab + b2)
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EX: FactorEX: Factor1. x3 – 8y3
2. x2 – 4x + 4
3. 4a2 – 25b4
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EX: Factor some more!EX: Factor some more!4. m4 - 81
5. 27r3 + 8v3
6. 64 – (x – y)2
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Guidelines for FactoringGuidelines for Factoring1. Check for a GCF2. 2 Terms: 2 Squares or 2 Cubes?◦ Squares: if they are subtracted, use the
difference of 2 squares formula.◦ Cubes: use either the sum of 3 cubes
formula or the difference of 2 cubes formula.
3. 3 Terms: Is it a perfect square?◦ YES: use Perfect Square Trinomial formula◦ NO: use REVERSE FOIL METHOD
4. 4 Terms: factor by GROUPING
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Examples… factor each Examples… factor each completelycompletely1. x2 – 8x + 152. 9x2 + 30x + 253. 24a5y – 2a4y2 – 12x3y3
4. x2y + 3x – xy2 – 3y5. 5m5 + 10m3n2 + 5mn4 6. (x + y)3 + (x – y)3