What is the standard form of # f=(x - 2)(x - y)^2 #?
2 Answers
Explanation:
To rewrite a function in standard form, expand the brackets:
#f(x)=(x-2)(x-y)^2#
#f(x)=(x-2)(x-y)(x-y)#
#f(x)=(x-2)(x^2-xy-xy+y^2)#
#f(x)=(x-2)(x^2-2xy+y^2)#
#f(x)=(x^3-2x^2y+xy^2-2x^2+4xy-2y^2)#
#f(x)=(x^3-2x^2y+xy^2-2x^2-2y^2+4xy)#
Attempted to make clear what is happening by using color
Explanation:
Given:
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider
Write as
This is distributive so we have:
Every part of the blue bracket is multiplied by all of the brown bracket:
Giving:
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute (2) into (1) for
Every part of the blue bracket is multiplied by all of the brown bracket:
Giving:
Changing the order giving x precedence over y