Question

Use distributive property to verify which expression is equivalent to parentheses (x - 5 )* (x - 3)

Answer 1

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the distributive property, we will apply the distributive property (also known as the FOIL method for binomials) to expand the expression.

1. **First**: Multiply the first terms in each binomial:
\[
x \cdot x = x^2
\]

2. **Outer**: Multiply the outer terms:
\[
x \cdot (-3) = -3x
\]

3. **Inner**: Multiply the inner terms:
\[
(-5) \cdot x = -5x
\]

4. **Last**: Multiply the last terms:
\[
(-5) \cdot (-3) = 15
\]

Now, add all these results together:
\[
x^2 - 3x - 5x + 15
\]

Combine the like terms (\(-3x\) and \(-5x\)):
\[
x^2 - 8x + 15
\]

Thus, the expression equivalent to \((x - 5)(x - 3)\) is:
\[
x^2 - 8x + 15
\]