To apply the distributive property to the expression [tex]\((x + 5)(x - 7)\)[/tex], we need to use the FOIL method, which stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial by each term in the second binomial. Let's go through each step:
1. First: Multiply the first terms in each binomial.
[tex]\[
x \cdot x = x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials.
[tex]\[
x \cdot (-7) = -7x
\][/tex]
3. Inner: Multiply the inner terms in the binomials.
[tex]\[
5 \cdot x = 5x
\][/tex]
4. Last: Multiply the last terms in each binomial.
[tex]\[
5 \cdot (-7) = -35
\][/tex]
Now, we combine these results:
[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 expression [tex]\((x + 5)(x - 7)\)[/tex] expanded using the distributive property is:
[tex]\[
x^2 - 2x - 35
\][/tex]
