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Collecting Like Terms
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 3a2 are not like terms, the first is a and the second is a2, 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 3x2+4x2 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? a2+ab−4ab+4a2
Simplify the expression x2+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?
Starting with the first part, how can we tidy up x3÷x?
We now have x2+4x×x+3x. Moving onto the second part, how do we tidy up 4x×x?
Now we have tidied up the expression to x2+4x2+3x we can see the like terms clearly. Take the last step to gather the like terms together.
Tidy up and simplify this expression.
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 x2 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 × or ÷ included. 4a×a needs to be multiplied out to 4a2 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.
x2+3x−4−4x+x2 can be simplified to 2x2−x−4 just by collecting like terms together.