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)

(2x - 5) (x + 7)

(2x) (x) + (2x) (7) + (-5) (x) + (-5) (7)

2x^2 + 9x - 35

2x^2 + 14x - 5x - 35

Answer 1

To multiply the binomials \((2x - 5)(x + 7)\) and simplify it, we follow these steps in order:

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

2. **Apply the distributive property (FOIL method):**
\[
(2x)(x) + (2x)(7) + (-5)(x) + (-5)(7)
\]

3. **Write out the products:**
\[
2x^2 + 14x - 5x - 35
\]

4. **Combine like terms:**
\[
2x^2 + 9x - 35
\]

So, the correct order of the steps is:

1. (2x - 5)(x + 7)
2. (2x)(x) + (2x)(7) + (-5)(x) + (-5)(7)
3. 2x^2 + 14x - 5x - 35
4. 2x^2 + 9x - 35