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

Question

□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: \[ \boxed{x^2 + 10x + 16} \]