To show that Expression 1 \((x - 5)(x + 3)\) is equivalent to Expression 2 \(2x^2 - x^2 - 2x - 20 + 5\) using the Distributive Property, we will simplify both expressions and see if they are equal.
Step 1: Simplify Expression 1
To simplify Expression 1: \[ (x - 5)(x + 3) = x(x + 3) - 5(x + 3) \] Now apply the distributive property: \[ = x^2 + 3x - 5x - 15 \] Combine like terms: \[ = x^2 - 2x - 15 \]
Step 2: Simplify Expression 2
Now, let's simplify Expression 2: The expression is \(2x^2 - x^2 - 2x - 20 + 5\). First, combine \(2x^2 - x^2\): \[ = x^2 - 2x - 20 + 5 \] Now combine the constant terms: \[ = x^2 - 2x - 15 \]
Conclusion:
Both expressions simplify to: \[ x^2 - 2x - 15 \] Thus, \((x - 5)(x + 3)\) is equivalent to \(2x^2 - x^2 - 2x - 20 + 5\) because when fully simplified, both expressions yield the exact same result of \(x^2 - 2x - 15\).