Certainly! Let's expand the expression [tex]\( (x + 2)(x - 4) \)[/tex] step by step.
1. Write the expression:
[tex]\[
(x + 2)(x - 4)
\][/tex]
2. Apply the distributive property (also known as the FOIL method for binomials):
[tex]\[
(x + 2)(x - 4) = x(x) + x(-4) + 2(x) + 2(-4)
\][/tex]
3. Multiply each pair:
[tex]\[
x \cdot x = x^2
\][/tex]
[tex]\[
x \cdot (-4) = -4x
\][/tex]
[tex]\[
2 \cdot x = 2x
\][/tex]
[tex]\[
2 \cdot (-4) = -8
\][/tex]
4. Combine all these products:
[tex]\[
(x + 2)(x - 4) = x^2 - 4x + 2x - 8
\][/tex]
5. Combine like terms:
[tex]\[
-4x + 2x = -2x
\][/tex]
6. Write the final expanded expression:
[tex]\[
x^2 - 2x - 8
\][/tex]
So, the expanded form of [tex]\( (x + 2)(x - 4) \)[/tex] is:
[tex]\[
x^2 - 2x - 8
\][/tex]
