Question

Multiply the binomials
(2x+8)(5x-7)

Answer 1

To multiply the binomials \( (2x + 8)(5x - 7) \), we can use the distributive property, often referred to as the FOIL method (First, Outside, Inside, Last).

1. **First**: Multiply the first terms:
\[
2x \cdot 5x = 10x^2
\]

2. **Outside**: Multiply the outer terms:
\[
2x \cdot (-7) = -14x
\]

3. **Inside**: Multiply the inner terms:
\[
8 \cdot 5x = 40x
\]

4. **Last**: Multiply the last terms:
\[
8 \cdot (-7) = -56
\]

Now, we combine all these results:
\[
10x^2 - 14x + 40x - 56
\]

Combine like terms:
\[
10x^2 + (40x - 14x) - 56 = 10x^2 + 26x - 56
\]

Thus, the product of the binomials \( (2x + 8)(5x - 7) \) is:
\[
\boxed{10x^2 + 26x - 56}
\]