# Simplifying an expression

We can often algebraic expressions by 'collecting like terms'.

Look at the expression $$2x + 5y + x - 3y$$

There are four terms $$2x,\,5y,\,x\,and\, - 3y.$$

Two of the terms involve $$x$$ and two involve $$y$$.

Now we can combine the $$x$$ terms and combine the $$y$$ terms to get $$3x + 2y$$.

## Example

Collect like terms and simplify this algebraic expression:

$a + 4b + 3a - 3b$

$$4a + b$$ ($$a+3a = 4a$$ and $$4b-3b = 1b$$)

Now have a go at simplifying the following expressions.

Question

$5a + 4b - a + b$

$= 4a + 5b$

Question

$4x - y - x + 2x$

$= 5x - y$

Question

$3m + n - m + 4n - 2m$

$= 0m + 5n$

$= 5n$

Now we combine multiplying out brackets and collecting like terms, to simplify algebraic expressions.

Question

Simplify $$3(x - 2y) + 4x$$

$= 3x - 6y + 4x$

$= 7x - 6y$

Question

Simplify $$3(x + y) + 2(x - y)$$

$= 3x + 3y + 2x - 2y$

$= 5x + y$