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factoring special products Formulas to memorize!

Learn and memorize important formulas for factoring special products, such as perfect square trinomials, difference of two squares, difference of two cubes, and sum of two cubes. Follow guidelines and examples to factor expressions completely.

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factoring special products Formulas to memorize!

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  1. Section 6.3 factoring special productsFormulas to memorize!

  2. FORMULAS… Memorize 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)

  3. EX: Factor • 1. x3 – 8y3 • 2. x2 – 4x + 4 • 3. 4a2 – 25b4

  4. EX: Factor some more! • 4. m4 - 81 • 5. 27r3 + 8v3 • 6. 64 – (x – y)2

  5. Guidelines for Factoring • 1. Check for a GCF • 2. 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

  6. Examples… factor each completely • 1. x2 – 8x + 15 • 2. 9x2 + 30x + 25 • 3. 24a5y – 2a4y2 – 12x3y3 • 4. x2y + 3x – xy2 – 3y • 5. 5m5 + 10m3n2 + 5mn4 • 6. (x + y)3 + (x – y)3

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