Chapter 9: Algebraic expressions and expanding brackets

You need to be able to work with algebraic expressions confidently

You can use the index laws to simplify algebraic expressions

You can square or cube a whole expression

Remember that if a letter appears on its own then it has the power 1

Algebraic expressions may also contain negative and fractional indices

When you are multiplying expressions:

Multiply any number parts first

Add the powers of each letter to work out the new power

When you are dividing expressions:

Divide any number parts first

Subtract the powers of each letter to work out the new power

Start by simplifying the top part of the fraction

Do the number part first then the powers

Next divide the expressions

Divide the number part, then divide the indices

Expanding or multiplying out brackets is a key algebra skill

You have to multiply the expression outside the bracket by everything inside the bracket

‘Expand and simplify’ means multiply out and then collect like terms

When you expand, you need to be careful with negative signs in front of the bracket

Negative signs belong to the term to their right

Multiply out the brackets first and then collect like terms if possible

You can use the grid method to expand two brackets

Or you can use the acronym FOIL to expand two brackets

Remembered as smiley face

First, outer, inner, last terms

If you have to multiply three factors, don’t try to do it all in one step

Expand and write brackets around the whole expansion

Then multiply every terms inside the brackets by x

You need to be able to work with algebraic expressions confidently

You can use the index laws to simplify algebraic expressions

You can square or cube a whole expression

Remember that if a letter appears on its own then it has the power 1

Algebraic expressions may also contain negative and fractional indices

When you are multiplying expressions:

Multiply any number parts first

Add the powers of each letter to work out the new power

When you are dividing expressions:

Divide any number parts first

Subtract the powers of each letter to work out the new power

Start by simplifying the top part of the fraction

Do the number part first then the powers

Next divide the expressions

Divide the number part, then divide the indices

Expanding or multiplying out brackets is a key algebra skill

You have to multiply the expression outside the bracket by everything inside the bracket

‘Expand and simplify’ means multiply out and then collect like terms

When you expand, you need to be careful with negative signs in front of the bracket

Negative signs belong to the term to their right

Multiply out the brackets first and then collect like terms if possible

You can use the grid method to expand two brackets

Or you can use the acronym FOIL to expand two brackets

Remembered as smiley face

First, outer, inner, last terms

If you have to multiply three factors, don’t try to do it all in one step

Expand and write brackets around the whole expansion

Then multiply every terms inside the brackets by x