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Here are some important algebra formulas for grade 12:

If a quadratic equation is given in the form ax² + bx + c = 0, the solutions for x can be found using the quadratic formula:

x = (-b ± √(b² – 4ac)) / 2a

2. Laws of Exponents:
a. am * an = a2(m+n)

b. (am)n = amn

c. (ab)n = an * bn

d. (a/b)n = an / bn

e. a(-n) = 1/an

3. Factorization Formulas:
a. Difference of Two Squares: a² – b² = (a+b)(a-b)

b. Perfect Square Trinomials: a² + 2ab + b² = (a+b)² and a² – 2ab + b² = (a-b)²

c. Sum and Difference of Two Cubes: a³ + b³ = (a+b)(a²-ab+b²) and a³ – b³ = (a-b)(a²+ab+b²)

4. Logarithmic Formulas:
a. log (xy) = log x + log y

b. log (x/y) = log x – log y

c. log (xa) = a log x

d. log (1/x) = – log x

e. log (a) + log (b) = log (ab)

f. log (a) – log (b) = log (a/b)

5. Binomial Theorem:
The binomial theorem gives the expansion of (a+b)n as:

(a+b)n = C(n, 0)an + C(n, 1)a(n-1)b + … + C(n, r)a(n-r)br + … + C(n, n)bn

where C(n, r) is the binomial coefficient, given by C(n, r) = n! / (r!(n-r)!).

These are some of the important algebra formulas for grade 12. It is important to practice and memorize these formulas to solve algebra problems easily and quickly.

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