To rewrite the polynomial \((x + 8)(x - 2)\) using the distributive property (also known as the FOIL method for binomials), we will distribute each term in the first binomial to each term in the second binomial:
\[ (x + 8)(x - 2) = x(x) + x(-2) + 8(x) + 8(-2) \]
Now, performing the multiplication step by step:
- \(x \cdot x = x^2\)
- \(x \cdot (-2) = -2x\)
- \(8 \cdot x = 8x\)
- \(8 \cdot (-2) = -16\)
Now, combine all the terms together:
\[ x^2 - 2x + 8x - 16 \]
Now, combine the like terms \(-2x\) and \(8x\):
\[ x^2 + 6x - 16 \]
So, the polynomial rewritten is:
\[ \boxed{x^2 + 6x - 16} \]