1. **Common Monomial Factoring**: Factor out the greatest common monomial factor from all terms. Formula: $$a x^m + b x^n = x^{\min(m,n)}(a x^{m-\min(m,n)} + b x^{n-\min(m,n)})$$ Easy tip: Find the largest factor common to all terms and factor it out. 2. **Factoring the Difference of Two Squares**: Use the identity $$a^2 - b^2 = (a - b)(a + b)$$ Easy tip: Recognize expressions as squares and subtracting, then apply the formula. 3. **Factoring Perfect Square Trinomials**: Use the identity $$a^2 \pm 2ab + b^2 = (a \pm b)^2$$ Easy tip: Check if first and last terms are perfect squares and middle term is twice the product. 4. **Factoring Quadratic Trinomials (a = 1)**: For $$x^2 + bx + c$$, find two numbers that multiply to $$c$$ and add to $$b$$. Formula: $$x^2 + bx + c = (x + m)(x + n)$$ where $$m+n=b$$ and $$mn=c$$ Easy tip: List factor pairs of $$c$$ and find the pair that sums to $$b$$. 5. **Factoring Quadratic Trinomials (a \neq 1)**: For $$ax^2 + bx + c$$, find two numbers that multiply to $$a c$$ and add to $$b$$, then split the middle term and factor by grouping. Easy tip: Multiply $$a$$ and $$c$$, find factors summing to $$b$$, rewrite middle term, then factor by grouping. 6. **Factoring the Sum or Difference of Two Cubes**: Sum: $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$ Difference: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ Easy tip: Recognize cubes and apply the formula directly. 7. **Factoring Completely**: Combine all above methods step-by-step until fully factored. Easy tip: Always factor out common factors first, then apply special formulas. 8. **Simplifying Rational Expressions**: Factor numerator and denominator completely, then cancel common factors. Easy tip: Factor fully before canceling to avoid mistakes. 9. **Multiplying and Dividing Rational Expressions**: Multiply numerators and denominators, factor completely, then simplify by canceling common factors. Easy tip: Factor first, then multiply or divide, then simplify. These formulas and tips will help you solve factoring problems efficiently and correctly every time.