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.