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

1 Answer
Dec 11, 2017

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.