# Forming Expressions

In exam questions, you are often asked to apply algebra to a particular topic – for example, the perimeter of a shape or the ages of different people. This is called forming expressions but it’s a very similar skill to forming equations.

Example 1
Find a simplified expression for the perimeter of the shape below.

The perimeter of a shape is the sum of the length of the sides so we simply add together all the lengths of the sides and simplify our expression.

Perimeter = 4𝑎 – 4 + 5 + 4𝑎 – 3 + 4𝑎 + 4𝑎
= 16𝑎 – 2

Example 2
Amee is four years older than Benji. Benji is twice as old as Charlie. Write a simplified expression for the sum of their ages.

The key to answering these questions is finding the age that doesn’t depend on anyone else’s age.

In this case, Amee’s age depends on Benji’s age (Amee is 4 years older) and Benji’s age depends on Charlie’s (Benji is twice as old). However, Charlie’s age doesn’t depend on anyone, so we assign a variable (a letter) to Charlie’s age: say 𝑎.

Now, we consider how we can express Benji’s age in terms of Charlie’s age. Benji is twice as old as Charlie, so we need to multiply Charlie’s age by 2.

So, Benji’s age is 2 × 𝑎 or 2𝑎.

Next, we consider how we can express Amee’s age in terms of Benji’s age. Amee is four years older than Benji so we need to add 4 to Benji’s age. Amee’s age is 2𝑎 + 4.

The question asks for the sum of their ages, so we need to add together the three ages and simplify the expression.

Sum of the ages = 2𝑎 + 4 + 2𝑎 + 𝑎
= 5𝑎 + 4

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