Grade 12 Algebra Formulas
Here are some important algebra formulas for grade 12:
1. Quadratic Formula:
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.