To apply the distributive property to the expression [tex]\((x+5)(x-7)\)[/tex], follow these steps:
1. Multiply each term in the first parentheses by each term in the second parentheses.
2. Combine all the resulting products.
Step-by-step process:
1. Multiply [tex]\(x\)[/tex] by [tex]\(x\)[/tex]:
[tex]\[
x \cdot x = x^2
\][/tex]
2. Multiply [tex]\(x\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
x \cdot (-7) = -7x
\][/tex]
3. Multiply [tex]\(5\)[/tex] by [tex]\(x\)[/tex]:
[tex]\[
5 \cdot x = 5x
\][/tex]
4. Multiply [tex]\(5\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
5 \cdot (-7) = -35
\][/tex]
Now, combine all the terms:
[tex]\[
x^2 + (-7x) + 5x + (-35)
\][/tex]
Combine like terms:
[tex]\[
x^2 - 7x + 5x - 35
\][/tex]
Simplify the expression:
[tex]\[
x^2 - 2x - 35
\][/tex]
So, after applying the distributive property to the expression [tex]\((x+5)(x-7)\)[/tex], we get:
[tex]\[
x^2 - 2x - 35
\][/tex]
