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# Deriving expressions

Sometimes we need to use a word based problem to write an expression.

If my rectangular garden is twice as long as it is wide, how can I express the area without knowing the side lengths?

We can turn statements like this into algebraic expressions.

Choose $x$ to represent the width of the garden. Then the length is $2x$. The area of a rectangle is the product of its side lengths, so the area is $2x \times x = 2x^2$.

The first thing to do is to represent the most basic quantity in the statement using a letter. Then write out any other quantities in terms of this letter. Work through the statement and "build up" the expression, remembering to use brackets if necessary.

I think of a number and add ten. Then I double the result. Give an expression for the new number in terms of the old one.

If we represent the original number using $n$, the first thing we do is to add $10$ to get to $n+10$. Then we multiply the entirety of this by $2$, to get $2(n+10)$.