Y.9 Edexcel

🔢 1. Factorization of Numbers (Arithmetic Factorization)

Breaking down a number into a product of its prime factors.

• Example:
  84=22×3×784 = 2^2 \times 3 \times 784=22×3×7

🧮 2. Factorization by Common Factors

Take out the greatest common factor (GCF) from all terms.

• Example:
  6×2+9x=3x(2x+3)6x^2 + 9x = 3x(2x + 3)6x2+9x=3x(2x+3)

🟦 3. Factoring Trinomials

Trinomials (3-term expressions) can often be factored into two binomials.

• Example:
  x2+5x+6=(x+2)(x+3)x^2 + 5x + 6 = (x + 2)(x + 3)x2+5x+6=(x+2)(x+3)

➖ 4. Difference of Squares

Used when an expression fits the pattern a2−b2a^2 – b^2a2−b2.

• Formula:
  a2−b2=(a−b)(a+b)a^2 – b^2 = (a – b)(a + b)a2−b2=(a−b)(a+b)

• Example:
  x2−16=(x−4)(x+4)x^2 – 16 = (x – 4)(x + 4)x2−16=(x−4)(x+4)

🔺 5. Perfect Square Trinomials

Special trinomials that are the square of a binomial.

• Formula:
  a2+2ab+b2=(a+b)2a^2 + 2ab + b^2 = (a + b)^2a2+2ab+b2=(a+b)2

• Example:
  x2+6x+9=(x+3)2x^2 + 6x + 9 = (x + 3)^2x2+6x+9=(x+3)2

🟰 6. Factoring by Grouping

Group terms in pairs and factor each group, then factor out the common binomial.

• Example:
  x3+3×2+2x+6=(x2+3x)(x+2)=(x+2)(x2+3x)x^3 + 3x^2 + 2x + 6 = (x^2 + 3x)(x + 2) = (x + 2)(x^2 + 3x)x3+3x2+2x+6=(x2+3x)(x+2)=(x+2)(x2+3x)

✳️ 7. Cubic Identities (Sum and Difference of Cubes)

Used for expressions like a3±b3a^3 \pm b^3a3±b3

• Formulas:
  a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a + b)(a^2 – ab + b^2)a3+b3=(a+b)(a2−ab+b2)
  a3−b3=(a−b)(a2+ab+b2)a^3 – b^3 = (a – b)(a^2 + ab + b^2)a3−b3=(a−b)(a2+ab+b2)

• Example:
  x3+8=(x+2)(x2−2x+4)x^3 + 8 = (x + 2)(x^2 – 2x + 4)x3+8=(x+2)(x2−2x+4)