Algebra

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Collecting Like Terms

By collecting like terms together, we can get equations into their simplest form.

Finding like terms and collecting them together makes equations much easier to read.

$4ab-ab+4$ is long. $3ab+4$ is simplified.

We identify like terms by the letters used in each term, the coefficients can be different.

$4ab$ and $3ba$ are like terms, we write each term in alphabetical order. $4a$ and $3a^2$ are not like terms, the first is $a$ and the second is $a^2$ , they are different.

Which two of these terms are like terms? Select two options.

You can select multiple answers

If we want to gather like terms together in the expression $3x^2+4x^2$ we need to add the coefficients. What is the answer here?

Simplify the expression $8xy+3yx-5xy$ .

What happens when an expression contains different terms?

We simplify as much as we can.

What is the simplified version of this expression? $a^2+ab-4ab+4a^2$

Simplify the expression $x^2+3x+5x+15$ .

It might be necessary to 'tidy up' an equation before gathering like terms.

We have already seen that terms should be in alphabetical order to see like terms clearly.

Which option 'tidies up' the expression $abc+2bac+3cab$ ?

Now we have $abc+2abc+3abc$ , it is much clearer that these are four like terms. What is the result of gathering them together?

Simplify $x^3\div x+4x\times x+3x$ .

Starting with the first part, how can we tidy up $x^3\div x$ ?

We now have $x^2+4x\times x+3x$ . Moving onto the second part, how do we tidy up $4x\times x$ ?

Now we have tidied up the expression to $x^2+4x^2+3x$ we can see the like terms clearly. Take the last step to gather the like terms together.

Tidy up and simplify this expression. $3a\times a+4a^3\div a+7a$
Take this step by step, tidying up first then finally gathering like terms together.

Summary! You can simplify algebraic expressions

You do that by collecting like terms.

Terms are separated by $+$ or $-$ .

Gather terms together by adding the coefficients, the number that multiplies the variables.

For example, $3ab+4ab$ contains like terms

they can be collected to give $7ab$

Remember that like terms can have different coefficients but must have the same variables.

$x$ and $x^2$ are different terms $a$ and $ab$ are different terms

You might need to 'tidy up' an expression before simplifying.

Complete terms if there are any $\times$ or $\div$ included. $4a\times a$ needs to be multiplied out to $4a^2$ first. Put terms in alphabetical order to see them clearly. $yzx$ and $zyx$ should both be $xyz$ so we can see they are the same.

Collecting like terms simplifies an expression or equation.

$x^2+3x-4-4x+x^2$ can be simplified to $2x^2-x-4$ just by collecting like terms together.