Index Laws

  • a^m * a^n = a^m+n
  • a^m / a^n = a^m-n
  • (a^m)^n = a^mn
  • (ab)^n = a^n * b^n

Expanding Brackets

  1. Multiply the x together 
  2. Add coefficients 
  3. Multiply the numbers 

Factorising

  • ax^2 +bx+c
  1. Find two factors of ac that add up to b 
  2. Rewrite the b term as a sum of these two factors 
  3. Factorise each pair of terms 
  4. Take out the common factor 
Difference of two squares
  • x^2 -y^2 = (x+y)(x-y)

Negative and Factorial Indices

  • a^1/m = msqrt(a)
  • a^n/m = msqrt(a^n)
  • a^-m = 1/a^m
  • a^0 = 1

 

Surds

Surds are irrational numbers 

sqrt(ab) = sqrt(a) * sqrt(b) 

sqrt(a/b) = sqrt(a)/sqrt(b) 

Rationalising denominators

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