Question

Multiply the binomials: (2x - 5) (x + 7)

Answer 1

To multiply the binomials \( (2x - 5)(x + 7) \), you can use the distributive property (also known as the FOIL method for binomials). Here’s how it works step by step:

1. **First:** Multiply the first terms:
\[
2x \cdot x = 2x^2
\]

2. **Outer:** Multiply the outer terms:
\[
2x \cdot 7 = 14x
\]

3. **Inner:** Multiply the inner terms:
\[
-5 \cdot x = -5x
\]

4. **Last:** Multiply the last terms:
\[
-5 \cdot 7 = -35
\]

Now, combine all these results:
\[
2x^2 + 14x - 5x - 35
\]

Next, combine the like terms \( 14x \) and \( -5x \):
\[
2x^2 + (14x - 5x) - 35 = 2x^2 + 9x - 35
\]

Therefore, the product of the binomials \( (2x - 5)(x + 7) \) is:
\[
\boxed{2x^2 + 9x - 35}
\]