Sure! Let's apply the distributive property step-by-step to the expression [tex]\((x+5)(x-7)\)[/tex].
1. First, distribute [tex]\(x\)[/tex] to each term in the second binomial:
[tex]\[
x(x - 7) + 5(x - 7)
\][/tex]
2. Now, distribute inside each parenthesis:
[tex]\[
x \cdot x + x \cdot (-7) + 5 \cdot x + 5 \cdot (-7)
\][/tex]
3. Perform the necessary multiplications:
[tex]\[
x^2 - 7x + 5x - 35
\][/tex]
4. 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] expands to [tex]\(x^2 - 2x - 35\)[/tex].
