Sure, let’s break this down step-by-step:
We are starting with the expression [tex]\((x+5)(x-7)\)[/tex].
1. First, apply the Distributive Property (also known as the FOIL method):
- First Terms: [tex]\(x \cdot x = x^2\)[/tex]
- Outer Terms: [tex]\(x \cdot (-7) = -7x\)[/tex]
- Inner Terms: [tex]\(5 \cdot x = 5x\)[/tex]
- Last Terms: [tex]\(5 \cdot (-7) = -35\)[/tex]
Putting these together, we have:
[tex]\[
x^2 - 7x + 5x - 35
\][/tex]
2. Next, combine like terms:
- Combine [tex]\(-7x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[
-7x + 5x = -2x
\][/tex]
So the final expression is:
[tex]\[
x^2 - 2x - 35
\][/tex]
So, the complete expression after applying the distributive property and simplifying is:
[tex]\[
x^2 - 2x - 35
\][/tex]
