Substitute negative values
Objective. Substitute directed numbers using brackets to protect signs.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Substituting a negative value into an expression requires enclosing it in brackets so the sign is applied correctly during multiplication or powers. For example, substituting x=−2 into 3x gives 3×(−2)=−6, and substituting into x² gives (−2)²=4, since a negative squared becomes positive. Without brackets, it is easy to misread the sign, especially with powers, so always write the substituted value in brackets first. Working through each operation in order, as with positive numbers, then gives the correct result.
Worked example
Evaluate 2x² + 5x when x = −3, substituting the negative value carefully.
- 1Substitute x=−3 using brackets: 2×(−3)²+5×(−3).
- 2Work out the power first: (−3)²=9.
- 3Multiply: 2×9=18 and 5×(−3)=−15.
- 4Add the results: 18+(−15)=3.
Answer: 3
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Practice
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Start practisingCommon mistake. Pupils often calculate −3² as 9 instead of −9 when a negative value is substituted without brackets around the base. Keep the substituted negative number inside brackets before applying any power.
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