Question

Can someone help me please

Answer 1

answer:

oops, I accidentally messed this one up, so sorry

Answer 2

Answer:

"We can't use any of the patterns"

Step-by-step explanation:

You can't use $(U+V)^2$ because that would result in some stuff in the middle. In general if you have something like that it would expand to $U^2+2UV + V^2$. and same thing for the (U-V)^2 except the middle would be a negative number. You also can't use $(U+V)(U-V)$ because it specifies "constant integers" and the "integer" part is what's really important, because you can technically rewrite the sum of squares as (U + V)(U - V) but you would need to use imaginary numbers. Because the difference of squares is defined as $a^2-b^2 = (a-b)(a+b)$. But you can also think of it like this $a-b = (\sqrt{a} - \sqrt{b})(\sqrt{a}+\sqrt{b})$ because that's essentially what the original identity is saying. Using this definition you can write the sum of squares as $a+b = a - (-b) = (\sqrt{a} + \sqrt{-b})(\sqrt{a} - \sqrt{-b}) = (\sqrt{a} + i\sqrt{b})(\sqrt{a} - i\sqrt{b})$. So with the restriction of constant integers "We can't use any of the patterns" is the correct answer