Verify the Equality: (x+8)(x-4) = (x-8)(x+4)

To determine if the equation $(x+8)(x-4) = (x-8)(x+4)$ is true, we'll need to expand both sides and compare their forms.

We begin with the left-hand side:

• $(x+8)(x-4)$

• Expanding using the distributive property, we get:

• $x \cdot x + x \cdot (-4) + 8 \cdot x + 8 \cdot (-4)$

• This simplifies to $x^2 - 4x + 8x - 32$

• Further simplification gives $x^2 + 4x - 32$

Now, let's examine the right-hand side:

• $(x-8)(x+4)$

• Expanding using the distributive property, we obtain:

• $x \cdot x + x \cdot 4 - 8 \cdot x - 8 \cdot 4$

• This simplifies to $x^2 + 4x - 8x - 32$

• Further simplification yields $x^2 - 4x - 32$

Next, compare the results:

The left-hand side is $x^2 + 4x - 32$, while the right-hand side is $x^2 - 4x - 32$.

Note that the coefficients of the $x$ terms are different:

• On the left: The coefficient of $x$ is $+4$.

• On the right: The coefficient of $x$ is $-4$.

Since the coefficients of$x$ differ, the two expressions are not equal.

Therefore, the equality $(x+8)(x-4) = (x-8)(x+4)$ is not correct.

The correct answer to this problem is No, the coefficients of $x$ in contrasting expressions.