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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)

1 answer

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

  1. Start with the given expression: (2x - 5)(x + 7)

  2. Use the distributive property (FOIL method) to multiply:

    • First: Multiply the first terms: \(2x \cdot x = 2x^2\)
    • Outer: Multiply the outer terms: \(2x \cdot 7 = 14x\)
    • Inner: Multiply the inner terms: \(-5 \cdot x = -5x\)
    • Last: Multiply the last terms: \(-5 \cdot 7 = -35\)

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

  4. Simplify by combining like terms: \(2x^2 + (14x - 5x) - 35\) which simplifies to \(2x^2 + 9x - 35\)

  5. End with the simplified trinomial: \(2x^2 + 9x - 35\)

So, the correct order of steps is:

  1. (2x - 5)(x + 7)
  2. Apply the distributive property (FOIL)
  3. Combine results: \(2x^2 + 14x - 5x - 35\)
  4. Simplify to: \(2x^2 + 9x - 35\)
  5. Final result: \(2x^2 + 9x - 35\)