Maths - brackets and indices

Maths - brackets and indices

1. Expanding and simplifying brackets

   • 9(3 - k) + 4(k - 1)
     • 27k - 9k + 4k-4 = 23 - 5k
   • Multiply out both brackets then simplify
   • 2b2*(3b - 4) - 2b(b - 3y)
     • 6b3* - 8b2* - 2b2* + 6by = 6b3 - 10b2* + 6by

2. Factorising expressions

   • Single brackets
     • 20y - 15 = 5(4y - 3)
     • 6w2*v + 2wv - 16w3*v2* = 2wv(3w + 1 - 8w2*v
     • Find the biggest denominator of all the numbers to put outside the brackets then inside the brackets divide each part of the expression by what is outside the brackets
   • Double brackets
     • You will need to use double brackets when there is squaring involved
     • x2* + 1x - 6
       • You need to start with 'x' in each of the brackets because x times x is x2*
         • (x)(x)
       • To factorise this successfully you need what you add next in to the brackets to ADD to make +1x and MULTIPLY to make -6
         • Find the factors of minus six and go through them until you get a pair to add to +1x
           • (x - 2)(x + 3)

3. Indices/ powers

   • The number or letter is the base and the small number at the top is the index
   • Multiplication
     • If the bases are the same you can add the powers together
     • If the bases are not the same times the bases and then add the powers and put them together
     • Brackets
       • If there is just a number or letter and a power in the bracket and another power outside just times the powers
       • If there is a number and a letter times everything in the bracket by the power outside
   • If something is to the power of 0* it is always 1
   • Division
     • If the bases are the same just take away the bottom power from the top but the number (or letter) stays the same
     • If the bases are different do the division with the numbers and then take away the powers