Expand the Binomial Product: (x+2)(x-4) Step-by-Step

In order to solve the given problem, we will use the FOIL method. FOIL stands for First, Outer, Inner, Last. This helps us to systematically expand the product of the two binomials:

• Step 1: Multiply the First terms.

The first terms of each binomial are $x$ and $x$. Multiply these together to obtain $x \times x = x^2$.

• Step 2: Multiply the Outer terms.

The outer terms are $x$ and $-4$. Multiply these. together to obtain $x \times -4 = -4x$.

• Step 3: Multiply the Inner terms.

The inner terms are $2$ and $x$. Multiply these together to obtain $2 \times x = 2x$.

• Step 4: Multiply the Last terms.

The last terms are $2$ and $-4$. Multiply these together to obtain $2 \times -4 = -8$.

Proceed to combine all these results together:

$x^2 - 4x + 2x - 8$

Finally, combine like terms:

Combine $-4x$ and $2x$ to obtain $-2x$.

The expanded form of the expression is therefore:

$x^2 - 2x - 8$

Thus, the solution to the problem is $x^2 - 2x - 8$, which corresponds to choice 1.