Factoring a mathematical expression means breaking it down into simpler components, called factors, which when multiplied together give the original expression. Here are the steps for factoring common types of expressions:

1. Factor Out the Greatest Common Factor (GCF):

• Find the greatest common factor (GCF) of all terms in the expression and factor it out.
• For example:
  $6x^2 + 9x$
  GCF is 3x, so we factor out $3x$:
  $3x(2x + 3)$

2. Factor Trinomials (Quadratics):

• For a quadratic expression of the form $ax^2 + bx + c$, find two numbers that multiply to $ac$ and add up to $b$.
• Example: $x^2 + 5x + 6$
  • Multiply $1 \times 6 = 6$
  • Find two numbers that multiply to 6 and add to 5 (which are 2 and 3).
  • So, $x^2 + 5x + 6 = (x + 2)(x + 3)$

3. Difference of Squares:

• For an expression of the form $a^2 - b^2$, it factors as $(a + b)(a - b)$.
• Example: $x^2 - 9 = (x + 3)(x - 3)$

4. Perfect Square Trinomial:

• For a trinomial of the form $a^2 + 2ab + b^2$, it factors as $(a + b)^2$.
• Example: $x^2 + 6x + 9 = (x + 3)^2$

5. Sum/Difference of Cubes:

• If the expression is $a^3 + b^3$, it factors as $(a + b)(a^2 - ab + b^2)$.
• For $a^3 - b^3$, it factors as $(a - b)(a^2 + ab + b^2)$.

Example: $x^3 - 8$ (since $8 = 2^3$)
$x^3 - 8 = (x - 2)(x^2 + 2x + 4)$

---

Would you like to practice factoring with a specific example, or do you have a particular expression you'd like help with?

Related Questions:

1. How do I factor trinomials with a leading coefficient greater than 1?
2. What do I do if there is no common factor in the terms of the expression?
3. How can I factor expressions with higher degrees, like quartic or cubic polynomials?
4. How do I identify the GCF when the terms have variables with different exponents?
5. Can all polynomials be factored into linear factors?

Tip: Always check for a GCF first before proceeding with other factoring methods.