To simplify the expression $(x - 5)(x - 3)$, use the distributive property (also known as FOIL for binomials):

$(x - 5)(x - 3) = x(x - 3) - 5(x - 3)$

Now distribute each term:

$= x^2 - 3x - 5x + 15$

Combine like terms:

$x^2 - 8x + 15$

So, $(x - 5)(x - 3) = x^2 - 8x + 15$.

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Related Questions:

1. How do you factor $x^2 - 8x + 15$?
2. What are the roots of the equation $x^2 - 8x + 15 = 0$?
3. How does the distributive property apply to polynomials?
4. What is the FOIL method in binomial multiplication?
5. Can you use this process with other binomials like $(x - 4)(x - 2)$?

Tip: Always group and combine like terms after distributing when multiplying polynomials!