Prime Factor decomposition
- A prime number is a number is a number with only 2 factors - itself and 1.
- Any number greater than 1 can be written as a product of its prime factors. this is called the prime factor decomposition of the number:
- 56 = 2 x 2 x 2 x 7= 2(3) x 7
Question: Express 84 as a product of its prime factors
- Don't include the times sign.
- Write divisions as fractions.
- write numbers first in products.
- Write letters in products of alpahbetical order.
Expanding brackets - Single
- to write an expression without brakets, multiply all the terms inside the bracket by the term outside.
- for negative terms, use the rules for multiplying by negative numbers:
negative term x positive term = negative term.
Expanding brackets - Double
- you can expand a double bracket in algebra by multiplying pairs of terms.
- each term in the first place
Multiplying expression (cont.)
Factorising single brackets
- To factorise an expression, you put the brackets in.
- you divide the terms by their highest common factor (HCF)
eg - 12x +24
HCF of 12x and 24 is 12.
12(x + 2)
Factorising Double brackets
- The two numbers in the brackets multiply to give the number at the end and add to give the number of xs
eg - ( x + 2 ) (x + 3 ) = x(2) + 3x + 2x + 6
= x(2) + 5x + 6 2 x 3 = 6 2+3=5
Approximation and rounding