How would the Expression (x^2+4)(y^2+4) be rewritten using two squares?

A) (2xy+4)^2+(2x+2y)^2
B) (xy-16)^2-(4x+4y)^2
C) (xy-2)^2-(2x+2y)^2
D) (xy-4)^2+(2x+2y)^2

Question

How would the Expression (x^2+4)(y^2+4) be rewritten using two squares?

A) (2xy+4)^2+(2x+2y)^2
B) (xy-16)^2-(4x+4y)^2
C) (xy-2)^2-(2x+2y)^2
D) (xy-4)^2+(2x+2y)^2

anonymous · Answer

@ganeshie8 can you help me please?

anonymous · Answer

@mathmate

anonymous · Answer

@Daugherty18 could you maybe help me? :)

mathmate · Answer

Hint:
First step: expand $ (x^2+4)(y^2+4) = x^2y^2+4y^2+4x^2+16 $
Notice that there are no xy terms.
You would choose a answer where there is no xy term, AND check the expanded answer correspond to the above expression.
For example, examine case (A),
$ (2xy+4)^2+(2x+2y)^2 = ...+16xy+...+8xy...$ so cannot be a solution.
To do the above, you need to do the OI of the FOIL process of multiplication of binomials, and that, for each of the squared terms.

Otherwise, expand each term and see if they match the expression given on the second line.

mathmate · Answer

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