Advanced Algebra Tricks

Quadratic equations can be solved quickly using formulas like the Vieta method or by completing the square in fewer steps. For example, if ax²+bx+c=0, instead of solving traditionally, try breaking b into two parts that multiply to ac and sum to b. This saves time in competitive exams.

Example: Solve 6x²+17x+12=0 → Split 17x into 8x+9x → Factorize → (3x+4)(2x+3)=0 → x=-4/3 or x=-3/2.

Factorization is essential for simplifying algebra problems. Recognize patterns like a² - b² = (a-b)(a+b) and a³ ± b³ = (a±b)(a² ∓ ab + b²). For quadratics, factorizing quickly helps avoid long division steps.

Example: 4x² - 25 = (2x - 5)(2x + 5) instantly using the difference of squares.

Many students forget to apply distributive property correctly or make sign errors when moving terms across the equation. Also, mixing up formulas for (a+b)² and (a-b)² is common.

Tip: Always double-check signs and simplify step-by-step instead of skipping intermediate steps.