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 $D)$ $2+x+y$