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. x. 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=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+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−5y, the subtract sign belongs to 5y.
Examples
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
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x2−4x+4 |
xy+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 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 1. In the example above, p means 1p. The number 1 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.
Perimeter =2m+2n
Example 2
Write an expression for the perimeter of the following shape. Simplify your answer as much as possible.
Perimeter =x+y+x+y+3x−y
Perimeter =5x+2y