Answer:
a + 8
Step-by-step explanation:
Note that
(x + y)² = x² + 2xy + y²
= x² + y² + 2xy
= a + 2(4) = a + 8
Here, we are required to determine an expression equal to (x + y)²
The correct answer is therefore (a + 8)
First, x² + y² = a can be rewritten completing the square method as;
(x+y) (x+y) = a + 2xy
when we expand the expression above; we have;
x² + 2xy + y² = a + 2xy
since, 2xy is present on both sides of the equation;
we still get the expression; x² + y² = a
Therefore, (x+y)² = a + 2xy
we can then substitute the value 4 for xy in the equation above;
Thus, since xy = 4, therefore 2xy = 8
Consequently, (x+y)² = a + 8
The correct answer is therefore (a + 8)
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