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Zorluk: KolayOperations on Polynomials

A square metal sheet has a side length of x+4x + 4 inches. A rectangular region with a width of xx inches and a length of x+2x + 2 inches is removed from the sheet. Which of the following expressions represents the area, in square inches, of the remaining portion of the sheet?

  1. A
    -2x + 16
  2. B
    8x + 14
  3. C
    10x + 16
  4. 6x + 16Cevap
  5. E
    6x + 8

Cevap

The expression that represents the remaining area is 6x+166x + 16.
To find the remaining area, subtract the area of the removed rectangle from the area of the original square sheet. The area of the square is (x+4)2=x2+8x+16(x + 4)^2 = x^2 + 8x + 16 and the area of the rectangle is x(x+2)=x2+2xx(x + 2) = x^2 + 2x. Subtracting these yields (x2+8x+16)−(x2+2x)=x2+8x+16−x2−2x=6x+16(x^2 + 8x + 16) - (x^2 + 2x) = x^2 + 8x + 16 - x^2 - 2x = 6x + 16.

Adım Adım Çözüm

1
Find the area of the original square metal sheet.
Area of the square is (x+4)2=x2+8x+16(x + 4)^2 = x^2 + 8x + 16 square inches.
The area of a square is calculated by squaring its side length.
2
Find the area of the removed rectangular region.
Area of the rectangle is x(x+2)=x2+2xx(x + 2) = x^2 + 2x square inches.
The area of a rectangle is calculated by multiplying its width by its length.
3
Subtract the area of the rectangular region from the area of the square sheet.
(x2+8x+16)−(x2+2x)=x2+8x+16−x2−2x=6x+16(x^2 + 8x + 16) - (x^2 + 2x) = x^2 + 8x + 16 - x^2 - 2x = 6x + 16 square inches.
Subtracting the removed area from the total area gives the remaining area, distributing the negative sign to all terms inside the parentheses.

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Operations on Polynomials
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Operations on Polynomials

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