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There are two sorts of number: prime numbers and non-prime, or composite, numbers. A composite number can be made by multiplying two or more prime numbers together. For example

<math>15 = 3 \times 5</math>

<math>6 = 2 \times 3</math>

We usually think of factors in pairs - 6 times 2 is 12. But 6 and 2 aren't the only factors of 12…

<math>6 \times 2</math>,<math>4 \times 3</math>,<math>1 \times 12</math>

…and there are also the negative numbers…

<math>-6 \times -2</math>,<math>-4 \times -3</math>,<math>-1 \times -12</math>

This same principle can also be applied to algebraic expressions. For example


can be split into two separate expressions that when multiplied together give <math>x^2-2x</math>…

<math>x \times (x-2)</math>

The key to factorising (or factoring) algebraic expressions is to look for factors (letters or numbers) that are common to each term. Hopefully in the example above you can see the common factor is simply <math>x</math>.

Factorise the following expressions:

  1. <math>4x+8</math>
  2. <math>2+2x</math>
  3. <math>xy+4x</math>
  4. <math>x+x^2</math>
  5. <math>20x^2+10x</math>
  6. <math>x-2x^2</math>
  7. <math>-ab+a^2b</math>
  8. <math>-2a-2b</math>

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