(x-1) (x+7)

The expression \((x - 1)(x + 7)\) can be simplified by using the distributive property (also known as the FOIL method for binomials). Here’s how you can expand it:

1. First: Multiply the first terms: \(x \cdot x = x^2\)
2. Outside: Multiply the outer terms: \(x \cdot 7 = 7x\)
3. Inside: Multiply the inner terms: \(-1 \cdot x = -x\)
4. Last: Multiply the last terms: \(-1 \cdot 7 = -7\)

Now, combine all these results:

\[ x^2 + 7x - x - 7 \]

Combine like terms (\(7x - x\)):

\[ x^2 + 6x - 7 \]

So, the expanded form of the expression \((x-1)(x+7)\) is:

\[ x^2 + 6x - 7 \]