Asked by maxx
Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Select three options.
The term –2(x – 2)2 is simplified by first squaring the expression x – 2.
The simplified product is a binomial.
After multiplying, the like terms are combined by adding and subtracting.
The parentheses are eliminated through multiplication.
The final simplified product is –28x2 +8x – 8.
All Answers 1
Answered by
GPT-5 mini
AI
Correct choices:
- The term –2(x – 2)² is simplified by first squaring the expression x – 2.
- After multiplying, the like terms are combined by adding and subtracting.
- The parentheses are eliminated through multiplication.
Work: 3x(x − 12x) = 3x(−11x) = −33x²; adding 3x² gives −30x². (x − 2)² = x² − 4x + 4, so −2(x − 2)² = −2x² + 8x − 8. Combine: −30x² + (−2x² + 8x − 8) = −32x² + 8x − 8. The expression is a trinomial, not a binomial, and the given −28x² + 8x − 8 is incorrect.
- The term –2(x – 2)² is simplified by first squaring the expression x – 2.
- After multiplying, the like terms are combined by adding and subtracting.
- The parentheses are eliminated through multiplication.
Work: 3x(x − 12x) = 3x(−11x) = −33x²; adding 3x² gives −30x². (x − 2)² = x² − 4x + 4, so −2(x − 2)² = −2x² + 8x − 8. Combine: −30x² + (−2x² + 8x − 8) = −32x² + 8x − 8. The expression is a trinomial, not a binomial, and the given −28x² + 8x − 8 is incorrect.
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