To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property, we can expand the expression.
\[ (x - 5)(x - 3) = x(x - 3) - 5(x - 3) \] First, distribute \(x\) and \(-5\):
\[ = x^2 - 3x - 5x + 15 \]
Combine like terms:
\[ = x^2 - 8x + 15 \]
Now, we will evaluate the given options:
- \(2x - 2\)
- \(x^2 - 8x + 15\)
- \(3x^2 - 4x^2 - 3x - 15\)
- \(x^2 - 2x + 15\)
The expression that matches our expanded expression \(x^2 - 8x + 15\) is:
\[ \text{Option 2: } x^2 - 8x + 15 \]
Now let's check option 3:
\[ 3x^2 - 4x^2 - 3x - 15 = (3x^2 - 4x^2) - 3x - 15 = -1x^2 - 3x - 15 \]
This does not match \(x^2 - 8x + 15\).
Options 1 and 4 do not match either, as both have different forms.
Thus, the expression that is equivalent to \((x - 5)(x - 3)\) is:
\[ \boxed{x^2 - 8x + 15} \]
1 answer