Question

Use the Distributive Property to verify which expression is equivalent to left parenthesis x minus 5 right parenthesis left parenthesis x minus 3 right parenthesis

Answer 1

To use the Distributive Property and verify which expression is equivalent to \((x - 5)(x - 3)\), we will expand this expression.

Using the Distributive Property, we multiply each term in the first parenthesis by each term in the second parenthesis:

\[
(x - 5)(x - 3) = x(x - 3) - 5(x - 3)
\]

Now distribute \(x\) in the first part:

\[
= x^2 - 3x
\]

Next, distribute \(-5\) in the second part:

\[
= -5x + 15
\]

Now combine the like terms:

\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]

Thus, the expression equivalent to \((x - 5)(x - 3)\) is:

\[
\boxed{x^2 - 8x + 15}
\]