Substitution into Expressions

What you will learn

• Replace letters with numbers.
• Use brackets for negative values.
• Follow the order of operations.

Before you start: you should know what a variable is and the order of operations. See Algebraic Expressions.

The idea

Substitution means putting a number in place of a letter. Once every letter has its value, the expression becomes an ordinary calculation.

Steps

1. Write the expression.
2. Replace each letter with its value, using brackets.
3. Work out powers, then multiplication and division, then addition and subtraction.

Negative values

Always put a negative value in brackets. $x^2$ with $x = -3$ is $(-3)^2 = 9$, but $-3^2$ means $-(3^2) = -9$. Brackets make the meaning clear.

Formulas are expressions

A formula such as $A = l \times w$ is substituted in the same way. Put in the known values and work out the unknown.

Worked examples

Example 1: One letter

Find $4a - 3$ when $a = 5$.

1. $4 \times 5 - 3$.
2. $20 - 3 = 17$.

Answer: $17$

Example 2: Two letters

Find $2x + 3y$ when $x = 4$ and $y = -2$.

1. $2(4) + 3(-2)$.
2. $8 - 6 = 2$.

Answer: $2$

Example 3: With a power

Find $x^2 + 2x$ when $x = -3$.

1. $(-3)^2 + 2(-3)$.
2. $9 - 6 = 3$.

Answer: $3$

Tip: write the expression again with brackets in place of each letter, then calculate.

Why it matters

Substitution is how you use formulas for area, speed, interest and temperature. It also tests whether two expressions are equal. Next, learn to simplify with like terms.