To find the expression equivalent to the given expression [tex]\((x+9)(x-2)-9x-6\)[/tex], we will follow a step-by-step process to simplify it.
1. Expand the product [tex]\((x+9)(x-2)\)[/tex]:
- Applying the distributive property (FOIL method:
[tex]\[
(x+9)(x-2) = x \cdot x + x \cdot (-2) + 9 \cdot x + 9 \cdot (-2)
\][/tex]
- This results in:
[tex]\[
x^2 - 2x + 9x - 18
\][/tex]
- Simplifying the middle terms:
[tex]\[
x^2 + 7x - 18
\][/tex]
2. Combine the expanded expression with the remaining terms of the original given expression [tex]\(-9x - 6\)[/tex]:
- Write it all together:
[tex]\[
x^2 + 7x - 18 - 9x - 6
\][/tex]
- Combine like terms:
[tex]\[
x^2 + (7x - 9x) - 18 - 6
\][/tex]
- This simplifies to:
[tex]\[
x^2 - 2x - 24
\][/tex]
Therefore, the equivalent expression to [tex]\((x+9)(x-2) - 9x - 6\)[/tex] is:
[tex]\[
x^2 - 2x - 24
\][/tex]
So, we find that [tex]\( (x+9)(x-2) - 9x - 6 \)[/tex] is simplified to [tex]\( (x-2)(x-12) \)[/tex], where you compare the equivalent expression form.
