8.5 Substitution into expressions and formulae — Learn

Prerequisites: substitution into simple expressions and the order of operations.

By the end of this section you can: substitute positive and negative values into expressions and formulae, then calculate accurately.

Covers: A2.

Learn the method

Substitution means replacing a letter with its given value. Put a negative value in brackets to protect its sign.

Then follow the order of operations: powers first, then multiplication and division, then addition and subtraction.

For $3x^2-2$ when $x=-2$, write $3(-2)^2-2=3\times4-2=10$.

A formula is an equation that shows a relationship. Substitute every stated value before calculating.

Worked example. Find $2x^2-3$ when $x=-4$.

$2(-4)^2-3$ — replace $x$ with $-4$.

$=2\times16-3$ — evaluate the power.

$=29$ — multiply, then subtract.

Watch out. Replacing $x$ with $-3$ does not make $x^2$ equal to $-9$. Use brackets: $(-3)^2=9$, then check the value in the original expression.

You should now be able to

• substitute positive and negative values into expressions and formulae, then calculate accurately.