Bitesize has changed! We're updating subjects as fast as we can. Visit our new site to find Bitesize guides and clips - and tell us what you think!
Print

Maths

Index notation

Index laws

Multiplying and dividing

When multiplying you add the indices, and when dividing you subtract the indices.

So it follows that:

p3 × p7 = p10, and s5 ÷ s3 = s2

For the expression:

4s3 x 3s2

The numbers in front of the variables follow the usual rules of multiplication and division, but index numbers follow the rules of indices. So we multiply 4 and 3 and add 3 and 2

4s3 × 3s2 = 12s5

Question

What is 3c2 × 5c4?

toggle answer

Answer

To work it out:

  • Add the indices:
  • 2 + 4 = 6
  • Multiply the numbers in front of the variable:
  • 3 x 5 = 15
  • Answer:
  • 3c2 × 5c4 = 15c6

Note: Take care when multiplying and dividing expressions such as y × y4 or z3 ÷ z.

y is the same as y1, so y × y4 = y5.

z is the same as z1, so z3 ÷ z = z2.

Adding and subtracting

You can only add and subtract 'like terms'.

3, 4 and 20 are all like terms (because they are all numbers).

a, 3a and 200a are all like terms (because they are all multiples of a).

a2, 10a2 and -2a2 are all like terms (because they are all multiples of a2)

You cannot simplify an expression like 4p + p2 because 4p and p2 are not like terms.

But you can simplify 3r2 + 5r2 + r2.

3r2 + 5r2 + r2 tells us that we have 'three lots of r2' + 'five lots of r2' + 'one lot of r2' - so in total 'nine lots of r2', or 9r2.

So, 3r2 + 5r2 + r 2 = 9r2

Question

What is s2 + 8s2 - 2s2?

toggle answer

Answer

Answer: 7s2

Remember that 1 + 8 - 2 = 7, so s2 + 8s2 - 2s2 = 7s2

Remember that if we have a mix of terms we must gather like terms before we simplify.

Example

3p2 + 2p + 4 - 2p2 + 5 = 3p2 - 2p2 + 2p + 4 + 5 = p2 + 2p + 9

Back to Algebra index

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.