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Maths

Simplifying algebraic expressions

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Simplifying algebraic expressions

​​In a nutshell

Algebraic terms which have the same letter are called 'like terms'. Like terms can be added or subtracted, e.g. 2x+3x=5x2x + 3x=5x. This is called simplifying. If terms have different letters, they cannot be simplified, e.g. 5x+3y5x+3y. Take care with ++ or -signs. The - belongs to the term it is in front of.


Example

In the expression 2x7t2x-7t, the - belongs to 7t7t.



Simplifying expressions

Terms with different powers cannot be added or subtracted..


Examples
5a+10b2a3b5a+10b-2a-3b​​
3a+7b3a+7b​​
3x2+2x3x^2+2x​​

cannot be simplified further

3x2+2xx2+7x3x^2+2x-x^2+7x​​
2x2+9x2x^2+9x​​
4xy+3x+xy4xy+3x+xy​​
3x+5xy3x+5xy​​


It is possible to use expressions to help you solve geometric problems.


Example 1

Write an expression for the perimeter of the following shape.



mm​​

nn​​
Maths; Algebraic manipulation; KS3 Year 7; Simplifying algebraic expressions


Perimeter =2m+2n=\underline{2m+2n}


Example 2

Write an expression for the perimeter of the following shape.  Simplify your answer as much as possible.


x+yx+y​​
Maths; Algebraic manipulation; KS3 Year 7; Simplifying algebraic expressions
x+yx+y​​
3xy3x-y​​


Perimeter =x+y+x+y+3xy=x+y+x+y+3x-y

Perimeter =5x+2y=\underline{5x+2y}

Frequently Asked Questions (FAQ)

FAQs

  • Question: Can you simplify terms with different letters?

    Answer: If terms have different letters, they cannot be simplified. For example, 2a+3b cannot be simplified further.

  • Question: How do you simplify expression in algebra?

    Answer: You can simplify expressions by adding or subtracting 'like terms'. Like terms contain the same letter or same combination of letters.

  • Question: What are 'like terms' in algebra?

    Answer: Algebraic terms which have the same letter are called 'like terms'. They can be added or subtracted.

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