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Simplifying algebraic expressions

Simplifying algebraic expressions

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Explainer Video

Tutor: Meera

Summary

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=5x2x+3x=5x. This is called simplifying. If terms have different letters, they cannot be simplified, e.g. 5x+3y5x+3y5x+3y. Take care with +++ or −-−signs. The −-− belongs to the term it is in front of.


Example

In the expression 2x−7t2x-7t2x−7t, the −-− belongs to 7t7t7t.



Simplifying expressions

Terms with different powers cannot be added or subtracted..


Examples

​5a+10b−2a−3b=3a+7b 3x2+2x=3x2+2x 3x2+2x−x2+7x=2x2+9x 4xy+3x+xy=3x+5xy\begin{aligned} 5a+10b-2a-3b&=3a+7b\\ \ \\3x^2+2x&=3x^2+2x \\ \ \\3x^2+2x-x^2+7x&=2x^2+9x\\ \ \\4xy+3x+xy&=3x+5xy\end{aligned}5a+10b−2a−3b 3x2+2x 3x2+2x−x2+7x 4xy+3x+xy​=3a+7b=3x2+2x=2x2+9x=3x+5xy​​​


Note: 3x2+2x3x^2 +2x3x2+2x cannot be simplified.​


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


Example 1

Write an expression for the perimeter of the following shape.
​mmm​​

​nnn​​
Maths; Algebra; KS4 Year 10; Simplifying algebraic expressions

Perimeter =2m+2n‾= \underline{2m+2n}=2m+2n​



Example 2

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


​x+yx+yx+y​​
Maths; Algebra; KS4 Year 10; Simplifying algebraic expressions
​x+yx+yx+y​​
​3x−y3x-y3x−y​​

Perimeter =x+y+x+y+3x−y=x+y+x+y+3x-y=x+y+x+y+3x−y

Perimeter =5x+2y‾=\underline{5x+2y}=5x+2y​

​


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Algebraic notation

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FAQs - Frequently Asked Questions

Can you simplify terms with different letters?

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

How do you simplify expression in algebra?

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

What are 'like terms' in algebra?

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

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