Simplifying an expression

We can often simplify 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

Answer

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