Evaluate the expression (2.75)3 – (2.00)3 – (0.75)3__________?
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Answer: D. 4.5 * 2.75
Explanation
The algebraic identity states that a cubed minus b cubed minus c cubed equals three abc when a equals b plus c. Testing the values shows that two point seven five equals two point zero zero plus zero point seven five. Applying the algebraic identity transforms the expression into three times two point zero zero times zero point seven five times two point seven five, simplifying to four point five times two point seven five. Algebraic factoring identities simplify complex polynomial expressions by recognizing underlying structural patterns. Cubic expansions and special binomial products are useful for solving advanced arithmetic calculation tests. Substitution methods allow complex decimal expressions to be evaluated without tedious manual multiplication.
Option A incorrectly repeats the primary term multiple times instead of applying the cross product identity. Option B isolates a single component variable incorrectly rather than representing the full factored identity. Option C misplaces the constant factors required by the standard cubic algebraic expansion formula.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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