Question

What is the standard form of `f=(x - 2)(x - 2)(x + y)(x - y)`?

Answer 1

To find the standard form of `f`, we need to first expand the brackets and rearrange them in a descending power of degree.

`f=(x-2)(x-2)(x+y)(x-y)`
`=(x-2)^2* (x+y)(x-y)`

we can use identities to expand it.
Identities :

`(a-b)^2=a^2-2ab+b^2`

`(a+b)(a-b)=a^2-b^2`

`f=(x^2-2(x)(2)+2^2)(x^2-y^2)`
`=(x^2-4x+4)(x^2-y^2)`
`=(x^2)(x^2-y^2)-4x(x^2-y^2)+4(x^2-y^2)`
`=x^4-x^2y^2-4x^3+4xy^2+4x^2-4y^2`

Remarks: `x^2y^2` have a degree of `4`, where `2` from `x^2` and `2` from `y^2`

As it is already in a descending degree of power, we don't have to rearrange it and it's the answer. Hope this can help you.