What is a factor of 4-(x+y)^2 and why?

Question

A) -(x+y)^2
B) x+y
C) 2-x+y
D) 2+x+y
E) 4+x+y

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Answer 1 · 2016-09-28T20:20:52

#color(green)(D") " 2+x+y)#

#(a^2-b^2)# can be factored as #(a+b)(a-b)#

If we let #color(blue)(a=2) rarr color(red)(a^2=4)#
and #color(blue)(b=x=y) rarr color(green)(b^2=(x+y)^2))#

Then #color(red)(4)-color(green)(""(x+y))= underline((2+(x+y)))(2-(x+y))#

Answer 2 · 2016-09-28T20:27:44

#D)##2+x+y#

In the given expression above we should factorize using this identity:

#color(blue)(a^2-b^2)=color(green)((a-b))color(brown)((a+b))#

#4-(x+y)^2#
#color(blue)(2^2-(x+y)^2)#

#=color(green)((2-(x+y)))color(brown)((2+(x+y)))#
#=color(green)((2-x-y))color(brown)((2+x+y))#

There are two factors:
#color(green)(2-x-y)# and #color(brown)(2+x+y)#

The choice in the given is the factor #D)## 2+x+y#