Question

which expression is equivalent to (w-8)(w+10)
a. w^2-80
b.w^2+2w-80
c.w^2+2w-18
d.w^2+10w

anonymous

Answer 1

To find an expression equivalent to \((w-8)(w+10)\), we will apply the distributive property (also known as the FOIL method for binomials).

Here are the steps:

1. **First**: Multiply the first terms:
\(w \cdot w = w^2\)

2. **Outer**: Multiply the outer terms:
\(w \cdot 10 = 10w\)

3. **Inner**: Multiply the inner terms:
\(-8 \cdot w = -8w\)

4. **Last**: Multiply the last terms:
\(-8 \cdot 10 = -80\)

Next, we combine all these results:

\[
w^2 + 10w - 8w - 80
\]

Combine the like terms (\(10w - 8w\)):

\[
w^2 + 2w - 80
\]

Thus, the expression equivalent to \((w-8)(w+10)\) is \(w^2 + 2w - 80\).

The correct answer is **b. \(w^2 + 2w - 80\)**.