Verify the Equation: (-4-x)(7+x) = -28-11x-x²

Is equality correct?

$(-4-x)(7+x)=-28-11x-x^2$

To solve this problem, we'll follow these steps:

• Step 1: Expand the expression on the left side using the distributive property

• Step 2: Simplify the expanded expression

• Step 3: Compare the simplified expression with the given expression on the right side

Now, let's work through each step:
Step 1: Expand using the distributive property. We apply the formula: $(a+b)(c+d) = ac + ad + bc + bd$.

For $(-4-x)(7+x)$, distribute each term:
$(-4)(7) + (-4)(x) + (-x)(7) + (-x)(x)$

Step 2: Simplify the terms:
$-28 - 4x - 7x - x^2$
Combine like terms: $-28 - 11x - x^2$

Step 3: Compare this with the given expression $-28 - 11x - x^2$. Both sides of the equation are identical, indicating the expressions are equivalent.

Therefore, the solution to the problem confirms the expressions are equal, and the correct choice is Yes.