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Ann wants to print and frame a photo she recently took at the beach. She plans for the print to have the dimensions 1010 inches by 88 inches, and she also plans to put a border around the photo that has an equal width all around.\newlineThe total area of the photo and border in square inches can be modeled by the expression (10+2x)(8+2x)(10 + 2x)(8 + 2x), where xx is the width of the border in inches. This expression can also be written in the form 4x2+36x+804x^2 + 36x + 80.\newlineWhat does the quantity 4x2+36x4x^2 + 36x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the border in inches\newline(B)the area of the photo in square inches\newline(C)the length of the photo and border together in inches\newline(D)the area of the border in square inches\newline

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Q. Ann wants to print and frame a photo she recently took at the beach. She plans for the print to have the dimensions 1010 inches by 88 inches, and she also plans to put a border around the photo that has an equal width all around.\newlineThe total area of the photo and border in square inches can be modeled by the expression (10+2x)(8+2x)(10 + 2x)(8 + 2x), where xx is the width of the border in inches. This expression can also be written in the form 4x2+36x+804x^2 + 36x + 80.\newlineWhat does the quantity 4x2+36x4x^2 + 36x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the border in inches\newline(B)the area of the photo in square inches\newline(C)the length of the photo and border together in inches\newline(D)the area of the border in square inches\newline
  1. Expand expression: The expression for the total area is (10+2x)(8+2x)(10 + 2x)(8 + 2x), which expands to 80+20x+16x+4x280 + 20x + 16x + 4x^2.
  2. Simplify expression: Simplify the expression to get 4x2+36x+804x^2 + 36x + 80.
  3. Identify photo area: The term 8080 represents the area of the photo itself, which is 1010 inches by 88 inches.
  4. Calculate border area: The terms 4x2+36x4x^2 + 36x represent the additional area added by the border.
  5. Choose correct answer: The correct choice that represents the area of the border in square inches is (D) the area of the border in square inches.

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