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Special Binomial Factoring

Special Binomial Factoring. By Christina Flavin. Types of Special Binomials. a 2 - b 2 : Difference of two squares a 3 + b 3 : Sum of two cubes a 3 – b 3 : Difference of two cubes. Solving a 2 - b 2.

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Special Binomial Factoring

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  1. Special Binomial Factoring By Christina Flavin

  2. Types of Special Binomials • a2 - b2 : Difference of two squares • a3 + b3 : Sum of two cubes • a3 – b3 : Difference of two cubes

  3. Solving a2 - b2 First take the square root of “a2” and “b2”Then take “a”& “b” and put them into the binomial form : (a-b)(a+b). Example: X2 – 16 √x2 = x √16 = 4, so “a” = x and “b” = 4. Now we put them into the binomial form. (x – 4)(x + 4)

  4. Solving a3 + b3 First find out what the perfect cube of “a” and “b” are. Once you find out what “a” and “b” are and then put them into the factor form of (a + b)(a2 – ab + b2). Example: x3 + 27 33 = 27 , so “a” = x and “b” = 3. Now we put it into the factored form. (x+3)(x2 – 3x + 9)

  5. Solving a3 – b3 The steps are similar to finding a3 + b3 how the ending factored form is different. First find out what the perfect cube of “a” and “b” are. Then take “a” and “b” and put them in the factored form (a – b)(a2 + ab + b2). Example: Y3 – 64 43 = 64, so “a” = y and “b” = 4. now put into the factored form (y – 4)(y2 + 4y + 16).

  6. Summary • Remember for the binomials a2 – b2 : the form is (a – b) (a + b) a3 + b3 : the form is (a + b)( a2 – ab + b2) a3 – b3 : the form is (a – b)(a2 + ab + b2)

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