Algebra
Substitution
Replace letters with values, then calculate.
Predict, test and explain
Step 1 of 3
Predict
If x = −3, what is 2x²?
Replace every occurrence of each letter with the same value. Brackets keep the sign of a negative value clear.
Explore and compare
Choose the investigation above. Predict what will change before you move a control.
Try it in the simulation. Change one thing at a time.
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Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
Evaluate the expression at the given value.
Hint
Put the negative input in brackets and calculate its square before multiplying.
Reveal answer
The square contributes eight and the linear term contributes six.
Build an explanation
Hint 1
Substitution replaces each letter with its given value. Keep the expression's operations in the same places.
Hint 2
Put negative values in brackets: if x = −4, write x² as (−4)² and 3x as 3 × (−4).
Hint 3
Calculate powers first, then multiplications, then additions and subtractions. In ax², square x before multiplying by a.
Worked example
This example uses fixed values, separate from the diagram controls.
With a = −2, b = 3, c = −1, x = −4 and y = 2, evaluate ax + by + c and ax² + bx + c.
- For ax + by + c, substitute to get (−2) × (−4) + 3 × 2 + (−1).
- The products are 8 and 6, so the first expression is 8 + 6 − 1 = 13.
- For ax² + bx + c, substitute to get (−2) × (−4)² + 3 × (−4) + (−1).
- (−4)² = 16. The second expression is −32 − 12 − 1 = −45.
Answer: ax + by + c = 13; ax² + bx + c = −45.
Connect this idea
Watch out: ax² means a × x², not (ax)². Brackets matter: (−4)² = 16, while −4² = −16.