Question

Use distributive property to rewrite the polynomial (x+8)(x+2).
□x²+□x+□

Answer 1

To use the distributive property (also known as the FOIL method for binomials), we can expand the expression \((x+8)(x+2)\).

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

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

3. **Inner**: Multiply the inner terms:
\[
8 \cdot x = 8x
\]

4. **Last**: Multiply the last terms:
\[
8 \cdot 2 = 16
\]

Now, combine these results:
\[
x^2 + 2x + 8x + 16
\]

Combine the like terms (\(2x\) and \(8x\)):
\[
x^2 + 10x + 16
\]

So, the polynomial can be rewritten as:
\[
\boxed{x^2 + 10x + 16}
\]