To improve your productivity, simplify the following expression using distributive property. \( (x-2)(x-8) \) \( x^{2}-10 x+16 \) \( 2 x-10 x+16 \) \( x^{2}+10 x-16 \) \( 2 x-16 x-10 \)

The expression \( (x-2)(x-8) \) can be simplified using the distributive property, often referred to as the FOIL method for binomials. By multiplying the first terms, outer terms, inner terms, and last terms, we get: \( x \cdot x = x^2 \), \( x \cdot (-8) = -8x \), \( -2 \cdot x = -2x \), and \( -2 \cdot (-8) = 16 \). Adding these together results in \( x^2 - 10x + 16 \). Many people mistakenly believe that the distributive property only applies to addition. However, it works beautifully with subtraction too! So when you see a binomial with a subtraction sign, don't shy away from using it. Just remember to multiply each component carefully, combine like terms, and voilà! You've transformed your expression into an elegant quadratic form.