FACTORING SPECIAL FACTORING SPECIAL PRODUCTSPRODUCTS

FORMULAS TO FORMULAS TO MEMORIZE!MEMORIZE!

Section 6.3

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)

EX: FactorEX: Factor1. x3 – 8y3

2. x2 – 4x + 4

3. 4a2 – 25b4

EX: Factor some more!EX: Factor some more!4. m4 - 81

5. 27r3 + 8v3

6. 64 – (x – y)2

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

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