Answer:
![\large\boxed{x^(2) -1}](https://img.qammunity.org/2023/formulas/mathematics/high-school/6xknw2jz1tzgjs5dt05t7nlvql2rbjcges.png)
Explanation:
How to multiply polynomials?
To multiply polynomials, apply the FOIL method, where:
Applying FOIL:
![(x+1)(x-1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/s9t3dxu1uwnvci4kmvta6dp8ng9ptj8tgh.png)
First
![x*x=x^(2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/be9psfiwqutfsdhhvps5gx4c0dpt8ajtpe.png)
Outside
![x*(-1)=-x](https://img.qammunity.org/2023/formulas/mathematics/high-school/3u2syoft07mqqfpnx7ys81617opd5oh26e.png)
Inside
![x*1=x](https://img.qammunity.org/2023/formulas/mathematics/high-school/zrcctr6gs1l5poilts79k5q07uv9oinccf.png)
Last
![1*(-1)=-1](https://img.qammunity.org/2023/formulas/mathematics/high-school/shvfg5skd2nf4d9wftwoj3eo7y0g46c8gn.png)
After applying FOIL I ended up with this answer:
.
You might notice that we can simplify this a bit by adding
and
. Their sum is
:
![x^(2) +0-1](https://img.qammunity.org/2023/formulas/mathematics/high-school/xet8hs0rbxjao8aonrlvhw7ct5b889lq6g.png)
![x^(2) -1](https://img.qammunity.org/2023/formulas/mathematics/high-school/hrv54ssf31neknez42kz2ni5p4yq74ihym.png)