IGCSE Maths / Working with algebra

Substituting into expressions and formulae revision notes

Edexcel International GCSE Maths (4MA1), chapter 4: Working with algebra, specification point 2.2a-f. Free lesson.

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Substitution means replacing letters in an expression with given numbers, then evaluating it. Brackets and the order of operations help you get the correct answer, especially when a value is negative.

How to substitute into an expression

Replace each letter with its value, putting the value in brackets. Then use the usual order of operations: powers first, then multiplication, then addition or subtraction. Brackets make clear which number a power applies to. For example, 3x² with x = 4 becomes 3(4)².

How to evaluate an expression with two values

When an expression has more than one letter, replace each letter with its given value. Work out the multiplications before adding.

Why negative values need brackets

A negative value must go in brackets so its sign stays attached to the number. This matters when the value is raised to a power. For example, (−3)² = 9, but −3² = −9 because the square applies to the 3 before the minus sign. An even power of a negative number is positive. After substituting, do powers before multiplication, then add or subtract.

What a number next to a letter means

A number written directly beside a letter means multiply. It does not mean write the digits next to each other. So 2x with x = 5 becomes 2 × 5 = 10, not 25.

Check a substitution with a negative value

For 3p² + 2p when p = −4, the squared value is positive, but the second term stays negative. Keeping the brackets while substituting helps you see both signs correctly. 3(−4)² + 2(−4) = 3 × 16 − 8 = 48 − 8 = 40.