Certainly! Let's apply the distributive property to the given expression step by step.
We start with the expression:
[tex]\[
(x + 5)(x - 7)
\][/tex]
To simplify this expression, we use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):
1. First: Multiply the first terms in each binomial:
[tex]\[
x \cdot x = x^2
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
x \cdot (-7) = -7x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
5 \cdot x = 5x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
5 \cdot (-7) = -35
\][/tex]
Now, we combine all these products:
[tex]\[
x^2 + (-7x) + 5x + (-35)
\][/tex]
Combine the like terms [tex]\(-7x\)[/tex] and [tex]\(5x\)[/tex]:
[tex]\[
x^2 - 2x - 35
\][/tex]
So, the expanded form of the expression [tex]\((x + 5)(x - 7)\)[/tex] using the distributive property is:
[tex]\[
x^2 - 2x - 35
\][/tex]
This concludes the step-by-step solution.
