Special Factoring Formulas

About Special Factoring Formulas

Let us first define factoring before learning about unique factoring formulas. An algebraic expression is factored when it is written as the product of two or more expressions. Factorization can be done in a variety of ways. One of them use unique factoring formulas.

What do you mean by Factoring Formulas?

As special factoring formulae, we use various algebraic formulas. By solving LHS and RHS of expression on both sides, these algebraic identities can be confirmed. The following are some factoring formulas that can be used:

  1. (a + b)2 = a2 + 2ab + b2
  2. (a - b)2 = a2 - 2ab + b2
  3. (a + b)3 =a3 + b3 + 3ab(a + b)
  4. (a - b)3 =a3 - b3 - 3ab(a - b)
  5. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
  6. (a - b)4 = a4 - 4a3b + 6a2b2 - 4ab3 + b4
  7. (a + b + c)2 = a2 + b2 +c2 + 2ab + 2ac + 2bc
  8. a2 – b2 = (a + b)(a – b)
  9. a2 + b2 = (a + b)2 - 2ab
  10. a3 – b3 = (a – b)(a2 + ab + b2)
  11. a3 + b3 = (a + b)(a2 - ab + b2)

Example: Factorize the given expression 8x3 + 27.

Sol: To factorize it 8x3 + 27.

We will use a3 + b3 formula (one of the special factoring formulas) to factorize this.

The given expression can be written as

8x3 + 27 = (2x)3 + 33

We will substitute a = 2x and b = 3 in the formula of a3 + b3.

a3 + b3 = (a + b)(a2 - ab + b2)

(2x)3+33 = (2x+3)((2x)2−(2x)(3)+32) = (2x+3)(4x2−6x+9)

Answer: 8x3 + 27 = (2x + 3) (4x2 - 6x + 9).

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Special Factoring Formulas

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