To rewrite the polynomial \((x + 8)(x - 2)\) using the distributive property, we apply the concept of distributing each term in the first parentheses to each term in the second parentheses:
-
Multiply \(x\) by \(x\): \[ x \cdot x = x^2 \]
-
Multiply \(x\) by \(-2\): \[ x \cdot -2 = -2x \]
-
Multiply \(8\) by \(x\): \[ 8 \cdot x = 8x \]
-
Multiply \(8\) by \(-2\): \[ 8 \cdot -2 = -16 \]
Now, combine all these results:
\[ x^2 - 2x + 8x - 16 \]
Next, combine the like terms \(-2x\) and \(8x\):
\[ x^2 + 6x - 16 \]
So, the polynomial \((x + 8)(x - 2)\) rewritten using the distributive property is:
\[ x^2 + 6x - 16 \]