Substitution with powers
Objective. Evaluate formulae containing powers and negative values.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Substitution with powers means replacing letters in a formula with given numbers, taking particular care with the order of operations when a power or a negative value is involved. When substituting a negative number into a squared term, such as finding x² when x = −3, calculate (−3)² = 9, since the whole negative value is squared, not just the 3. In a formula like y = 2x² + 5, substituting x = −3 gives y = 2 × 9 + 5 = 23, applying the power before the multiplication, following BIDMAS throughout.
Worked example
Find the value of 3x² − 4 when x = −2, using substitution with powers.
- 1Substitute x = −2 into the squared term: (−2)² = 4
- 2Multiply by the coefficient: 3 × 4 = 12
- 3Subtract 4 from the result: 12 − 4
- 4Calculate the final value: 8
Answer: 8
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Practice
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Start practisingCommon mistake. Pupils often calculate x² for x = −3 as −9 by squaring only the 3 and keeping the negative sign separately, instead of correctly squaring the whole negative value to get (−3)² = 9.
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