Question

Can someone help me please

Answer 1

oops, I accidentally messed this one up, so sorry

Answer 2

"We can't use any of the patterns"

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 = (√(a) - √(b))(√(a)+√(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) = (√(a) + √(-b))(√(a) - √(-b)) = (√(a) + i√(b))(√(a) - i√(b))`. So with the restriction of constant integers "We can't use any of the patterns" is the correct answer