Set 6: Quadratic Equations (Intermediate)

Explanation

Answer: B

A square picture frame has a border of width 2 inches. If the inner picture has side length $x$ , what is the area of the entire frame (picture + border)?

$x^2 + 4x + 4$

$x^2 + 8x + 16$

✓ Correct

$x^2 + 4$

$x^2 + 16$

Detailed Explanation

Choice B is correct. Choice B is the correct answer. 1. The inner side is $x$ . 2. The border adds 2 inches to the left and 2 inches to the right (or top/bottom). So the total side length is $x + 2 + 2 = x + 4$ . 3. The area of the entire square is $(x + 4)^2$ . 4. Expand: $x^2 + 8 x + 16$ . Choice A is incorrect because it assumes the border is only on one side ( $x+2$ ). Choice C is incorrect because it forgets the middle term. Choice D is incorrect because it forgets the middle term.

Key Steps:

•

The correct answer is $x^2 + 8x + 16$

Why others are wrong:

A: Choice A is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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