Verify the Equation: (x+5)(x+3) = x²-3²

To assess whether the equation $(x+5)(x+3) = x^2 - 3^2$ is a true or false statement, we follow these steps:

• Step 1: Expand the left side using distributive property (FOIL).
• Step 2: Simplify the expression.
• Step 3: Simplify the right side.
• Step 4: Compare both sides of the equation.

Step 1: Expand $(x+5)(x+3)$:
$(x+5)(x+3) = x(x+3) + 5(x+3)$
$= x^2 + 3x + 5x + 15$

Step 2: Simplify this expression:
$x^2 + 3x + 5x + 15 = x^2 + 8x + 15$

Step 3: Evaluate the right side:
$x^2 - 3^2 = x^2 - 9$

Step 4: Compare $x^2 + 8x + 15$ to $x^2 - 9$:
Clearly, $x^2 + 8x + 15 \neq x^2 - 9$, as the former includes the terms $8x + 15$, while the latter is simply reduced by 9.

Therefore, the equation $(x+5)(x+3) = x^2 - 3^2$ is a Lie (false statement) because the left and right sides do not match for any value of $x$.