Certainly! Let's expand the expression [tex]\((x - 5)(x + 6)\)[/tex] step-by-step.
1. Use the distributive property (FOIL method):
To expand [tex]\((x - 5)(x + 6)\)[/tex], we will multiply each term in the first binomial by each term in the second binomial.
[tex]\[
(x - 5)(x + 6) = x \cdot x + x \cdot 6 + (-5) \cdot x + (-5) \cdot 6
\][/tex]
2. Multiply the terms:
- [tex]\(x \cdot x = x^2\)[/tex]
- [tex]\(x \cdot 6 = 6x\)[/tex]
- [tex]\((-5) \cdot x = -5x\)[/tex]
- [tex]\((-5) \cdot 6 = -30\)[/tex]
Putting it all together, we get:
[tex]\[
x^2 + 6x - 5x - 30
\][/tex]
3. Combine like terms:
The like terms here are [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex]. Adding these gives:
[tex]\[
6x - 5x = x
\][/tex]
So now we have:
[tex]\[
x^2 + x - 30
\][/tex]
Therefore, the expanded form of the expression [tex]\((x - 5)(x + 6)\)[/tex] is:
[tex]\[
\boxed{x^2 + x - 30}
\][/tex]
This is the final answer.
