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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

Algebra uses a combination of letters and numbers to derive expressions called terms. It helps to find unknown quantities. If there is an unknown quantity, start by giving it a letter name, e.g. xxx. This can then be used in an expression, equation or formula. 



Terms

Terms are a combination of numbers and letters. Algebraic terms which have the same letter are called 'like terms' and can be added or subtracted, e.g. 2x+3x=5x2x +3x=5x2x+3x=5x. This is called simplifying. If terms have different letters, or a different combination of letters, they cannot be added or subtracted, e.g. 2x+3y2x+3y2x+3y cannot be simplified further.


Note: Take care with negatives. The subtract sign belongs to the term it sits in front of. E.g. In 2x−5y2x -5y2x−5y, the subtract sign belongs to 5y5y5y.


Examples

​2×x=2x 8×t=8t −5×y=−5y 3×n×n=3n2\begin{aligned}2\times x&=2x\\ \ \\8\times t&=8t\\ \ \\-5\times y&=-5y\\ \ \\3\times n\times n&=3n^2\end{aligned}2×x 8×t −5×y 3×n×n​=2x=8t=−5y=3n2​​​



Expressions

An expression is a string of terms separated by a +++ or −-−.

​

Examples
​2x+2y2x+2y2x+2y​​
​a−2ba-2ba−2b​​
​x2−4x+4x^2-4x+4x2−4x+4​​
​xy+x2+3y+1xy+x^2+3y+1xy+x2+3y+1​​



Simplifying expressions

Expressions can be simplified by adding or subtracting various terms. Terms with different powers cannot be added or subtracted.


Note: In order to be combined, two terms should be made of the same letter or same combination of letters.


Examples

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


Note: if a term has no number in front of it, it is assumed to be 111. In the example above, ppp means 1p1p1p. The number 111 is usually omitted.​


It is possible to simplify expressions to help us 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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FAQs - Frequently Asked Questions

What are 'like terms' in algebra?

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

What is an expression?

An expression is a string of terms, usually separated by addition or subtraction. For example, 2x +3y.

What is a variable?

A variable is an unknown quantity. We can name it with a letter, e.g. 'x' , and then use it in calculations.

What are terms in algebra?

A term is usually a combination of numbers and letters, e.g. 2x. Once we have a term, it can be used in an expression, equation or formula to help us find unknown quantities.

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