ACT Preparation / Unit 8 ACT 0722 worked example, 60 to 90 seconds
Recognizing an Equivalent Expression
The idea
When a question asks which expression is equivalent to a given one, work in three steps. First, simplify the given expression: expand products, combine like terms, or factor and cancel. Second, simplify each choice the same way, or compare it with the simplified form. Third, if two choices look close, substitute a number, such as x = 2, into the original and each choice; an equivalent expression matches every time.
In practice
Worked example: which is equivalent to (x + 3)² − (x − 3)²? Expanding gives x² + 6x + 9 − x² + 6x − 9 = 12x. The choices are 0, 18, 12x and 2x² + 18; only 12x matches. Check at x = 2: 5² − (−1)² = 24, and 12 × 2 = 24, while 2x² + 18 gives 26.
Where people slip
A substitution can rule a choice out with one mismatch, but one match proves little. Avoid testing with 0 or 1, where many different expressions agree.
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