b. \( (x-4)(x-2)= \)

To expand the expression \( (x-4)(x-2) \), you simply apply the distributive property, or FOIL method. Multiplying the first terms gives you \( x^2 \), then multiplying the outer terms results in \( -2x \). Moving on to the inner terms, you get \( -4x \), and finally, multiplying the last terms gives \( +8 \). So, when you combine like terms, your final result is \( x^2 - 6x + 8 \). Now, did you know that factoring expressions like \( (x-4)(x-2) \) can be reversed to find the roots of a quadratic equation? When you set each factor to zero, \( x-4=0 \) and \( x-2=0 \), you find the solutions \( x=4 \) and \( x=2 \). This is a fundamental skill in algebra, converting factored forms back to standard forms, and is an essential technique in solving quadratic equations!