What is the correct standard form of the equation

Question

√(x+4)2+(y−2)2
explain each step

Answer 1

The given expression is √(x+4)2+(y−2)2.

To write it in standard form, start by expanding the square terms:

(x+4)2 = (x+4)(x+4) = x2 + 8x + 16

(y−2)2 = (y−2)(y−2) = y2 − 4y + 4

So the expression becomes:

√(x2 + 8x + 16 + y2 − 4y + 4)

Combining like terms inside the square root:

√(x2 + y2 + 8x − 4y + 16 + 4)

Simplifying further:

√(x2 + y2 + 8x − 4y + 20)

This is the expression in standard form.