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 \(3(x + y) + 2(x - y)\)

\[= 3x + 3y + 2x - 2y\]

\[= 5x + y\]