Question

Put the steps in the correct order when multiplying the binomials: (2x−5)(x+7)
. Start with the given expression and end with the simplified trinomial.(4 points)
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Answer 1

To multiply the binomials \( (2x - 5)(x + 7) \), you can follow these steps in the correct order:

1. **Distribute** \(2x\) to both terms in the second binomial:
- \(2x \cdot x = 2x^2\)
- \(2x \cdot 7 = 14x\)

2. **Distribute** \(-5\) to both terms in the second binomial:
- \(-5 \cdot x = -5x\)
- \(-5 \cdot 7 = -35\)

3. **Combine** all the results from the distributions:
- \(2x^2 + 14x - 5x - 35\)

4. **Simplify** the expression by combining like terms:
- \(2x^2 + (14x - 5x) - 35 = 2x^2 + 9x - 35\)

Thus, the final simplified trinomial is \(2x^2 + 9x - 35\).