Albert Teen

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Collecting Like Terms

# Collecting Like Terms

### Collecting Like Terms

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

1

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

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

2

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.

3

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

4

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 $8xy+3yx-5xy$.

1

What happens when an expression contains different terms?

We simplify as much as we can.

2

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

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

1

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.

2

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

3

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

1

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

2

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

3

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.

1

Summary! You can simplify algebraic expressions

You do that by collecting like terms.

2

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

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

3

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

they can be collected to give $7ab$

4

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

5

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.

6

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.