Question

question 7 of 10
how would the expression \\((x^2 + 1)(y^2 + 4)\\) be rewritten using two squares?

\\(\bigcirc\\) a. \\((xy - 2)^2 + (x + 2y)^2\\)
\\(\bigcirc\\) b. \\((xy + 2)^2 + (x + 2y)^2\\)
\\(\bigcirc\\) c. \\((xy - 2)^2 - (4x + y)^2\\)
\\(\bigcirc\\) d. \\((xy - 2)^2 + (2x + y)^2\\)

Explanation:

Step1: Expand original expression

$(x^2 + 1)(y^2 + 4) = x^2y^2 + 4x^2 + y^2 + 4$

Step2: Expand option D

$(xy - 2)^2 + (2x + y)^2 = (x^2y^2 - 4xy + 4) + (4x^2 + 4xy + y^2) = x^2y^2 + 4x^2 + y^2 + 4$

Step3: Match results

Expanded option D equals original expression.

Answer:

D. $(xy - 2)^2 + (2x + y)^2$